Question 11 Mark
Find a quadratic polynomial, the sum and product of whose zeroes are $0,\sqrt 5 $ respectively.
Answer
View full question & answer→Let the polynomial be $ax^2 + bx + c,$
and its zeroes be $\alpha $ and $\beta $.
Then, $\alpha + \beta = 0 = - \frac { b } { a } \text { and } \alpha \beta = \sqrt { 5 } = \frac { c } { a }$
If a = 1, then b = 0 and $c = \sqrt { 5 }$.
So, one quadratic polynomial which fits the given conditions is $x ^ { 2 } + \sqrt { 5 }$ .
and its zeroes be $\alpha $ and $\beta $.
Then, $\alpha + \beta = 0 = - \frac { b } { a } \text { and } \alpha \beta = \sqrt { 5 } = \frac { c } { a }$
If a = 1, then b = 0 and $c = \sqrt { 5 }$.
So, one quadratic polynomial which fits the given conditions is $x ^ { 2 } + \sqrt { 5 }$ .
