Question

Find a quadratic equation with sum and product of its zeroes are √3 and -5 respectively

Answer 1

Answer:

Quadratic equation are written as x^2 - Sx + P = 0, where S is the sum of roots and P is the product of roots.

Here,

S = sum of roots = $\sqrt3$

P = product of roots = - 5

Hence, eq. is -

= > x^2 - $\sqrt3$ x - 5 = 0

Using quadractic formula to check whether I am correct or not.

= > x = $\dfrac{-(-\sqrt3 )\pm\sqrt{3-4(-5)}}{2}$

= > x = $\dfrac{\sqrt3 \pm \sqrt{23}}{2}$

Now,

sum of values of x = $\dfrac{\sqrt3 + \sqrt{23}}{2}$+ $\dfrac{\sqrt3 - \sqrt{23}}{2}$

sum of roots = 2 $\sqrt3$

product of values of x = $\bigg(\dfrac{\sqrt3 + \sqrt{23}}{2} \bigg)\bigg(\dfrac{\sqrt3 - \sqrt{23}}{2}\bigg)$

product of roots = ( 3 - 23 ) / 4 = - 20/4 = - 5

Hence verified as well.

therefore, eq. is x^2 - $\sqrt3$ - 5 = 0

Answer 2

Given,

Sum of the zeroes , S = √3

Product of the zeroes, P = - 5

Required polynomial = k ( x² - S x + P)

= x² - √3 x -5, where k= 1

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