Question

Find the zeroes of P(x) = 2x2 – X – 6 and
verify the relationship of zeroes with the coefficient.​

Answer 1

Step-by-step explanation:

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Answer 2

By factorization method

$P(x) => 2x^2 - x - 6 = 0$

$→ 2x^2 - x - 6 = 0$

$→ 2x^2 - 4x + 3x - 6 = 0$

$→ 2x(x - 2) + 3(x-2) = 0$

$→ (2x+3) (x-2) = 0$

$x = \dfrac{-3}{2} \:and \: x = 2$

$\alpha = \dfrac{-3}{2}$ and $\beta = 2$

Relationship

$P(x) => 2x^2 - x - 6 = 0$

Here, $a = 2 , b = -1 , c = -6$

________________

$\alpha + \beta = \dfrac{-b}{a}$

$\dfrac{-3}{2} + 2 = \dfrac{-(-1)}{2}$

$\dfrac{-3+4}{2} = \dfrac{1}{2}$

$\dfrac{1}{2} = \dfrac{1}{2}$ Verified✔️

________________

$\alpha × \beta = \dfrac{c}{a}$

$\dfrac{-3}{2} × 2 = \dfrac{-6}{2}$

$\dfrac{-6}{2} = \dfrac{-6}{2}$

$-3 = -3$ verified✔️