Question

Find the zeroes of the quadratic polynomial 6x²-5x-14 and verify both relations.​

Answer 1

Step-by-step explanation:

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2 and - 7/6

Given polynomial :

6x² - 5x - 14

We can find the zeroes of the quadratic polynomial by splitting the middle term. To split the middle term, we need two numbers whose sum is (-5) and product is (14 * 6 = 84).

Such two numbers can be (-12) and (7).

Here we go,

Therefore, the zeroes of the quadratic polynomial is 2 and -7/6.

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Answer 2

GIVEN

Find the zeroes of the quadratic polynomial 6x²-5x-14 and verify both relations

SOLUTION

Splitting middle term

➢ 6x² - 5x - 14 = 0

➢ 6x² - 12x + 7x - 14 = 0

➢ 6x(x - 2) + 7(x - 2) = 0

➢ (x - 2)(6x + 7) = 0

Either

➢ (x - 2) = 0

➢ x = 2

Or

➢ (6x + 7) = 0

➢ x = -7/6

Hence, 2 and -7/6 are the zeros of given polynomial

Verification

${\boxed{\bf{\red{Sum\:of\:zeros}}}}$

$\implies\sf \dfrac{-(coefficient\:of\:x)}{coefficient\:of\:x^2}=\dfrac{- b}{a} \\ \\ \\ \sf =-2 + \dfrac{(-7)}{6}=\dfrac{12-7}{6} = \dfrac{-5}{6}$

${\boxed{\bf{\red{Product\:of\:zeros}}}}$

$\implies\sf \dfrac{(Constant\:term)}{coefficient\:of\:x^2}=\dfrac{c}{a} \\ \\ \\ \sf =2\times{\dfrac{(-7)}{6}} = \dfrac{-14}{6}$