Question 11 Mark
If $\alpha, \beta$are zeroes of the polynomial $p(x)=5 x^2-6 x+1$ then find the value of $\alpha+\beta+\alpha \beta$
Answer
View full question & answer→$7 / 5$
Questions
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Test yourself on this topic
37 questions · timed · auto-graded
Question 21 Mark
If $\alpha, \beta$ are the zeros of the polynomial $2 y^2+7 y+5$ write the value of $\alpha+\beta+\alpha \beta$.
Answer
View full question & answer→-1
Question 31 Mark
For what value of k, is -2 a zero of the polynomial $3 x^2+4 x+2 k$?
Answer
View full question & answer→-2
Question 41 Mark
For what value of k, is - 3 a zero of the polynomial $x^2+11 x+k$?
Answer
View full question & answer→24
Question 51 Mark
For what value of k, is 3 a zero of the polynomial $2 x^2+x+k$?
Answer
View full question & answer→-21
Question 61 Mark
If $\alpha, \beta$ are the zeros of a polynomial such that $\alpha+\beta=-6$ and $\alpha \beta=-4$, then write the polynomial.
Answer
View full question & answer→$f(x)=x^2+6 x-4$
Question 71 Mark
For what value of k, - 4 is a zero of the polynomial $x^2-x-(2 k+2) ?$
Answer
View full question & answer→9
Question 81 Mark
If (x + a) is a factor of $2 x^2+2 a x+5 x+10$ find a.
Answer
View full question & answer→2
Question 91 Mark
Write the zeros of the polynomial $x^2-x-6$.
Answer
View full question & answer→3,-2
Question 101 Mark
Answer
View full question & answer→c < 0
Question 111 Mark
The graph of the polynomial $f(x)=a x^2+b x+c$ is as shown below (Fig.)Write the signs of c.
Answer
View full question & answer→c > 0
Question 121 Mark
Answer
View full question & answer→$b^2-4 a c=0$, Two
Question 131 Mark
Answer
View full question & answer→$a>0, b^2-4 a c>0$
Question 141 Mark
If fourth degree polynomial is divided by a quadratic polynomial, write the degree of the remainder.
Answer
View full question & answer→Less than or equal to 1
Question 151 Mark
If $f(x)=x^3+x^2-a x+b$ is divisible by $x^2-x$ write the values of a and b.
Answer
View full question & answer→a = 2 b = 0
Question 161 Mark
If f(x) is a polynomial such that f(a) f(b) < 0 then what is the number of zeros lying between a and b?
Answer
View full question & answer→At least one
Question 171 Mark
If graph of quadratic polynomial $a x^2+b x+c$ cuts positive direction of y-axis, then what is the sign of c?
Answer
View full question & answer→Positive
Question 181 Mark
If the graph of quadratic polynomial $a x^2+b x+c$ cuts negative direction of y-axis, then what is the sign of c?
Answer
View full question & answer→Negative
Question 191 Mark
If a quadratic polynomial f (x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f (x)?
Answer
View full question & answer→2
Question 201 Mark
If 1 is a zero of the polynomial $p(x)=a x^2-3(a-1) x-1$ then find the value of a.
Answer
View full question & answer→1
Question 211 Mark
Write the coefficients of the polynomial $p(z)=z^5-2 z^2+4$.
Answer
View full question & answer→1, 0, 0, -2, 0, 4
Question 221 Mark
Write a quadratic polynomial, sum of whose zeros is $2 \sqrt{3}$ and their product is 2.
Answer
View full question & answer→$f(x)=x^2-2 \sqrt{3} x+2$
Question 231 Mark
If x = 1 is a zero of the polynomial $f(x)=x^3-2 x^2+4 x+k$, write the value of k.
Answer
View full question & answer→k = -3
Question 241 Mark
Answer
View full question & answer→4
Question 251 Mark
Answer
View full question & answer→3
Question 261 Mark
In Fig., the graph of a polynomial p(x) is given. Find the zeros of the polynomial.
Answer
View full question & answer→-3.5 and -1
Question 271 Mark
If the sum of the zeros of the quadratic polynomial $f(x)=k x^2-3 x+5$ is 1 write the value of k.
Answer
View full question & answer→3
Question 281 Mark
If the product of zeros of the quadratic polynomial $f(x)=x^2-4 x+k$ is 3,find the value of k.
Answer
View full question & answer→k = 3
Question 291 Mark
Write the family of quadratic polynomials having $-\frac{1}{4}$ and 1 as its zeros.
Answer
View full question & answer→$f(x)=k\left(x^2-\frac{3}{4} x-\frac{1}{4}\right)$ where k is any non-zero real number.
Question 301 Mark
The sum and product of the zeros of a quadratic polynomial are $-\frac{1}{2}$ and -3 respectively. What is the quadratic polynomial.
Answer
View full question & answer→$f(x)=k\left(x^2+\frac{x}{2}-3\right)$,where k is any non-zero real number.
Question 311 Mark
Define zero of a polynomial.
Answer
View full question & answer→self
Question 321 Mark
Define value of a polynomial at a point.
Answer
View full question & answer→self
Question 331 Mark
Write the standard form of a cubic polynomial with real coefficients.
Answer
View full question & answer→$f(x)=a x^3+b x^2+c x+d, a \neq 0$
Question 341 Mark
Write the standard form of a quadratic polynomial with real coefficients.
Answer
View full question & answer→$f(x)=a x^2+b x+c, a \neq 0$
Question 351 Mark
Write the standard form of a linear polynomial with real coefficients.
Answer
View full question & answer→$f(x)=a x+b, a \neq 0$
Question 361 Mark
Define degree of a polynomial.
Answer
View full question & answer→self
Question 371 Mark
Define a polynomial with real coefficients.
Answer
View full question & answer→self