Question

Find the zeros of the polynomail and hence verify the relationship between the zeros and co-efficent 2x²-x-6

Answer 1

Answer:

2x square-x-6

2x square-4x+3x-6

2x(x-2)+3(x-2)

(x-2) (2x+3)

x is equal to 2 or x is equal to -3/2

you can check the zeros by the formulae given in the book itself

Answer 2

$\underline\mathfrak\pink{Given:-}$

• $\: \: \: \: \: P \: {(x)} \: \: = \: \: {2x}^{2} \: - \: {x} \: - \: {6}$

$\underline\mathfrak\pink{To \: \: Find:-}$

• Zeroes of polynomial.
• Relationship between the zeroes are coefficients.

$\underline\mathfrak\pink{Solutions:-}$

• $\: \: \: \: \: P \: {(x)} \: \: = \: \: {2x}^{2} \: - \: {x} \: - \: {6}$

$\: \: \: \: \: \leadsto \: \: {2x}^{2} \: - \: {x} \: - \: {6}$

$\: \: \: \: \: \leadsto \: \: {2x}^{2} \: - \: {4x} \: + \: {3x} \: - \: {6}$

$\: \: \: \: \: \leadsto \: \: {2x} \: {({x} \: - \: {2})} \: + \: {3} \: {({x} \: - \: {2})}$

$\: \: \: \: \: \leadsto \: \: {({2x} \: + \: {3})} \: \: \: {({x} \: - \: {2})}$

$\: \: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: \frac{-3}{2} \: \: \: and \: \: \: {x} \: \: = \: \: {2}$

• $\: \: \: \: \: \: \: \: \: {\alpha} \: \: = \: \: \frac{-3}{2} \: \: \: and \: \: \: {\beta} \: \: = \: \: {2}$

$\underline\mathfrak\pink{Verification:-}$

$\: \: \: \: \: P \: {(x)} \: \: = \: \: {2x}^{2} \: - \: {x} \: - \: {6}$

• a = 2
• b = -1
• c = -6

$\: \: \: \: \: \therefore \: \: {\alpha} \: + \: {\beta} \: \: = \: \: \frac{-b}{a}$

$\: \: \: \: \: \leadsto \: \: \frac{-3}{2} \: + \: {2} \: \: = \: \: \frac{- \: {(-1)}}{2}$

$\: \: \: \: \: \leadsto \: \: \frac{{-3} \: + \: {4}}{2} \: \: = \: \: \frac{1}{2}$

$\: \: \: \: \: \leadsto \: \: \frac{1}{2} \: \: = \: \: \frac{1}{2}$

$\: \: \: \: \: \therefore \: \: {\alpha} \: {\beta} \: \: = \: \: \frac{c}{a}$

$\: \: \: \: \: \leadsto \: \: \frac{-3}{2} \: \times \: {2} \: \: = \: \: \frac{-6}{2}$

$\: \: \: \: \: \leadsto \: \: \frac{-6}{2} \: \: = \: \: \frac{-6}{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: {Verified.}$

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