Sample QuestionsQuadratic Equations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The roots of the quadratic equation $2 x^2-x-6=0$ are
- A
$-2, \frac{3}{2}$
- ✓
$2,-\frac{3}{2}$
- C
$-2,-\frac{3}{2}$
- D
$2, \frac{3}{2}$
Answer: B.
View full solution →The roots of the equation $x^2+x-p(p+1)=0$ where $p$ is a constant, are
- A
$p, p+1$
- B
$-p, p+1$
- ✓
$p,-(p+1)$
- D
$-p,-(p+1)$
Answer: C.
View full solution →If the quadratic equation $a x^2+b x+c=0$ has two real and equal roots, then $'c\ '$ is equal to
- A
$\frac{- b }{2 a }$
- B
$\frac{ b }{2 a }$
- C
$\frac{-b^2}{4 a}$
- ✓
$\frac{ b ^2}{4 a }$
Answer: D.
View full solution →The roots of the quadratic equation $x^2-0.04=0$ are
Answer: A.
View full solution →A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option :
Assertion (A) : If one root of the quadratic equation $4 x^2-10 x+(k-4)=0$ is reciprocal of the other, then value of k is 8 .
Reason $( R )$ : Roots of the quadratic equation $x ^2- x +1=0$ are real.
- A
(a) Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).
- B
(b) Both Assertion (A) and Reason (R) are true but Reason (R) does not give the correct explanation of Assertion (A).
- ✓
(c) Assertion (A) is true but Reason (R) is false.
- D
(d) Assertion (A) is false but Reason (R) is true.
Answer: C.
View full solution →If the quadratic equation $p x^2-2 \sqrt{5} p x+15=0$ has two equal roots, Then find the value of $p$.
View full solution →If $x=-\frac{1}{2}$, is a solution of the quadratic equation $3 x^2+2 k x-3=0$, find the value of $k .$
View full solution →Solve the quadratic equation $2 x^2+a x-a^2=0$ for $x$.
View full solution →If $2$ is a zero of the polynomial $a x^2-2 x$, then the value of $'a\ '$ is $......$
View full solution →Find the value of $k$ for which the quadratic equation $kx ( x -2)+6=0$ has two equal roots.
View full solution →Find the value of $k$ for which the equation $x^2+k(2 x+k-1)+2=0$ has real and equal roots.
View full solution →Find the roots of the quadratic equation $\sqrt{2} x^2+7 x+5 \sqrt{2}=0$
View full solution →Find the value of $p$ so that the quadratic equation $p x(x-3)+9=0$ has two equal roots.
View full solution →If $-5$ is a root of the quadratic equation $2 x^2+p x-15=0$ and the quadratic equation $p \left( x ^2+ x \right)+ k =0$ has equal roots, find the value of $k$.
View full solution →If $x=\frac{2}{3}$ and $x=-3$ are roots of the quadratic equation $a x^2+7 x+b=0$, find thevalues of $a$ and $b$.
View full solution →Is it possible to design a rectangular park of perimeter $80 m$ and area $400 m^2$ ? If so find its length and breadth.
View full solution →If the equation $\left(1+m^2\right) x^2+2 m c x+c^2-a^2=0$ has equal roots then show that $c^2=a^2\left(1+m^2\right)$.
View full solution →If $a d \neq b c$, then prove that the equation $\left(a^2+b^2\right) x^2+2(a c+b d) x+\left(c^2+d^2\right)=0$ has no real roots.
View full solution →Solve for $x, x^2-(2 b-1) x+\left(b^2-b-20\right)=0$
View full solution →Solve for $x, \frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}, x \neq-4,7$.
View full solution →Two taps running together can fill a tank in $3 \frac{1}{13}$ hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?
View full solution →Solve for $x$ :
$\frac{1}{x+1}+\frac{3}{5 x+1}=\frac{5}{x+4}, x \neq-1,-\frac{1}{5},-4$
View full solution →A motor boat whose speed is $24 km / h$ in still water takes 1 hour more to 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
View full solution →Solve for $x$ :
$\frac{1}{x+1}+\frac{2}{x+2}=\frac{4}{x+4}, x \neq-1,-2,-4$
View full solution →If $\alpha$ and $\beta$ are the zeros of the polynomial $f(x)=x^2-6 x+k$, find the value of k for $\alpha^2+\beta^2=40$.
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