Question

if the roots of a quadratic equation are 4 and -5 form the quadratic equation​

Answer 1

Answer:

$= {x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes) \\= {x}^{2} - (4 - 5)x + (4 \times - 5) \\= {x}^{2} + x - 20$

Answer 2

Answer:

x² - x - 20

Step-by-step explanation:

We know form of Quadratic equation as

x² - (å+ñ)x + åñ If å and ñ ane roots of the equation

Given that å = 4 and ñ = -5

so Sum of roots is 4-5 = -1

And Product of roots is (4)(-5) = -20

So equation formed is

x² + x -20

We can also find it in an another way. i.e.

If 4 and -5 are roots of equation then

(x-4) and (x+5) are factors of equation

So equation formed will be

p(x) = (x-4)(x+5)

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

= x² + 5x - 4x - 20

= x² + x - 20