Question

Find the zeroes of the quadratic polynomial Plx) = x2+x-12 and
verify the relationship between the zeroes and the coefficients.​

Answer 1

Answer:

Given,

→ p(x) = x² + x - 12

We have to find out the roots of this equation and also verify the relationship between zeros and coefficients.

So,

→ x² + x - 12 = 0

Splitting the middle term, we get,

→ x² - 3x + 4x - 12 = 0

→ x(x - 3) + 4(x - 3) = 0

→ (x + 4)(x - 3) = 0

→ (x + 4) = 0 or (x - 3) = 0

So,

→ x = 3, -4

Now, standard form of quadratic equation is -

→ ax² + bx + c = 0

Let m and n be the roots of this equation. So,

→ m + n = -b/a and,

→ mn = c/a

In the given quadratic equation,

→ a = 1

→ b = 1

→ c = -12

Now,

-4 + 3 = 1 and -4 × 3 = -12

Also,

-b/a = -1/1 = -1 and c/a = -12/1 = -12

Thus, the relationship holds true (Verified)

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