Question

find the qudratic polynomial whose zeros are 3 and -5

Answer 1

Step-by-step explanation:

given zeroes are 3 and -5

required one

(x-3)(x+5)=0

$x ^{2} - 3x + 5 x - 15 = 0$

$x ^{2} + 2x - 15 = 0$

x^2+2x-15=0

is the required answer....

I hope it helps you.....

Answer 2

Step-by-step explanation:

here we have given the zeros of the quadratic polynomial 3 and -5

let us consider the zeros are α and β

α = 3

β = - 5

we know the formula to making a quadratic polynomial whose zeroes are α and β

x² - (α + β )x + (α x β )

x² - (3 + (-5))x + ( 3 x (-5))

x² - (-2)x + (-15)

x² + 2x - 15

therefor the quadratic polynomial is x² + 2x - 15 = 0

Verification :

put the values of zeros as a x = 3 and x = -5 in the above equation and equate it with zero

put x = 3

x² + 2x - 15 = 0

(3)² + 2 (3) - 15 = 0

9 + 6 - 15 = 0

15 - 15 = 0

0 = 0

Now, x = -5

x² + 2x - 15 = 0

(-5)² + 2 (-5) - 15 = 0

25 - 10 - 15 = 0

25 - 25 = 0

0 = 0

hence verified