Question

Find the zeros of quadratic polynomial and verify the relationship between the zeros and coefficient
x²-17x-60​

Answer 1

SOLUTION.

Here, the equation is,

→ x² - 17x - 60 = 0

By splitting the middle term, we get,

→ x² - 20x + 3x - 60 = 0

→ x(x - 20) + 3(x - 20) = 0

→ (x + 3)(x - 20) = 0

By zero-product rule,

→ Either (x + 3) = 0 or (x - 20) = 0

→ x = -3, 20

★ So, the roots of the given equation are – -3 and 20.

VERIFICATION.

The standard form of a quadratic equation is –

→ ax² + bx + c = 0

Comparing the given equation with the standard form, we get,

→ a = 1

→ b = -17

→ c = -60

We know that,

→ Sum of roots = -b/a

→ Product of roots = c/aa

Here,

→ Sum of roots = -3 + 20 = 17

Also, using formula, we get,

Sum = -(-17)/1 = 17

Now,

→ Product of zeros = -3 × 20 = -60

Again, product using formula is -

= c/a

= -60/1

= -60

Hence, Verified.