Question

Find the quadratic polynomials, sum of whose zeroes is - 8 and their products is 16. Hence find the zeroes.

Answer 1

Hey dear !!

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==> Answer !!

Let the quadratic polynomial be ax² + bx + c .

Also we assume its zeroes are α and β

According to the given condition

α + β = -8

And

αβ = 16

∴ The required quadratic polynomial

=> x² - (α + β )x + αβ

=> x² - (-8)x + 16

=> x² + 8x + 16

Therefore,the required quadratic polynomial according to the given condition is [ x² + 8x + 16 ]

Now, zeroes of the quadratic polynomial .

=> x² + 8x + 16

=> x² + 4x + 4x + 16

=> x(x + 4) + 4(x + 4)

=> (x + 4 ) (x + 4 )

∴ x + 4 = 0

∴ x = -4

Therefore, -4 and -4 are the zeroes of the polynomial .

Thanks !!!

[ Be Brainly ]

Answer 2

Hey!

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Let 'a' and 'b' be the zeroes of the quadratic polynomial.

Given -:

a + b = -8

a × b = 16

Let p (x) be the quadratic equation,

p (x) = x^2 + ( sum of zeroes) x + ( product of zeroes)

= x^2 - ( -8) x + (16)

= x^2 + 8x + 16

Now, splitting the middle term -:

x^2 + 4x + 4x + 16

(x^2 + 4x ) + (4x + 16)

= x (x + 4) + x (x + 4)

= (x+ 4) (x+ 4)

Thus, two zeroes are -4 and -4

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Hope it helps...!!!