Question

Find a quadratic polynomial whose zeroes are -5 , -3

Answer 1

Answer:

a+b= -5+(-3)= -8

ab= (-5)(-3)= 15

x^2- (a+b)x+ ab

x^2+ 8x+ 15

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Answer 2

Given:-

• Zeroes of a quadratic polynomial = -5 and -3

To Find:-

• The quadratic polynomial

Solution:-

Let the two zeroes be α and β such that:-

• Sum of zeroes = α + β
• Product of zeroes = αβ

Hence,

α + β = (-5) + (-3)

⇒ α + β = -5 - 3

⇒ α + β = -8

Now,

αβ = (-5) × (-3)

⇒ αβ = 15

∴ We got:-

• α + β = -8 . . . . . . . (i)
• αβ = 15 . . . . . . . . . (ii)

We know,

A quadratic polynomial is in the form:-

• x² - (α + β)x + αβ . . . . . . . . . (iii)

Putting the values from equation (i) and equation (ii) in equation (iii)

= x² - (-8)x + 15

= x² + 8x + 15

∴ The required quadratic polynomial is x² + 8x + 15.

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Verification!!!

Let us find the zeroes of the polynomial we got.

= x² + 8x + 15

By splitting middle term,

= x² + 5x + 3x + 15

Taking common terms out,

= x(x + 5) + 3(x + 5)

= (x + 3)(x + 5)

Either,

x + 3 = 0

⇒ x = -3

Or,

x + 5 = 0

⇒ x = -5

Hence, we can see that we got two zeroes as -3 and -5 as per stated in the question.

Hence Verified!!!

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