Question

if root are 4 and -5 then create quadratic equation​

Answer 1

Given   : root are 4 and -5

To Find : create quadratic equation​

Solution:

root are 4 and -5

quadratic equation​

= (x - 4)(x - (-5))

= (x - 4)(x + 5)

= x² + 5x - 4x - 20

= x² + x - 20

Method 2

root are 4 and -5

Sum of roots = - 1

product of roots = - 20

Equation x² - (sum of roots)x + Product of roots = 0

=> x² - (-1)x + (-20) = 0

=> x² + x - 20 = 0

x² + x - 20 is required quadratic equation​

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Answer 2

SOLUTION

TO DETERMINE

The quadratic equation whose root are 4 and - 5

CONCEPT TO BE IMPLEMENTED

If the zeroes of a quadratic equation are given then the quadratic equation is

$\sf{{x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes } = 0$

EVALUATION

Here it is given that the roots / zeroes are 4 , - 5

Sum of the zeroes = - 5 + 4 = - 1

Product of the zeroes = - 5 × 4 = - 20

So the required Quadratic equation is

$\sf{{x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes } = 0$

$\implies \sf{ {x}^{2} - ( - 1)x - 20 = 0}$

$\implies \sf{ {x}^{2} + x - 20 = 0}$

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