Question

3. Find the zeroes of the quadratic polynomial and verify the relation between
the zeroes and its coefficient
x2 + 8x + 15

Answer 1

Answer:

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Answer 2

Given, quadratic polynomial is x² + 8x + 15.

We have to find the zeros the quadratic polynomial and verify the relation between the zeroes and its coefficient.

Now, the above equation is in the form ax² + bx + c = 0.

We have to find a number whose sum is b i.e. 8 and product is ac i.e. 15*1

→ x² + 8x + 15 = 0

→ x² + 5x + 3x + 15 = 0

→ x(x + 5) + 3(x + 5) = 0

→ (x + 5) (x + 3) = 0

On comparing we get,

→ x = -5, -3

Therefore, the zeros the quadratic polynomial is -5 and -3.

Verification

We know that,

Sum of zeros = -b/a and Product of zeros = c/a

And in given quadatic polynomial i.e. x² + 8x + 15.

a = 1, b = 8 and c = 15

Now,

Sum of zeros = -b/a

-5 + (-3) = -8/1

-5 - 3 = -8

-8 = -8

Product of zeros = c/a

(-5) × (-3) = 15/1

15 = 15