Question

(Q:16) If one root of the equation X2-9X+M=0, exceeds the other by 3, then the value of M is equal to​

Answer 1

Given info : one root of the equation x² - 9x + M = 0 exceeds the other by 3.

To find : the value of M is ...

solution : let one root of the given equation is α then the other root is α + 3.

now sum of roots = α + α + 3 = - coefficient of x/coefficient of x² = -(-9)/1

⇒ 2α + 3 = 9

⇒ α = 3

now the product of roots = α(α + 3) = constant/coefficient of x² = M/1

⇒ 3(3 + 3) = M

⇒ M = 18

therefore the value of M is 18.

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Answer 2

Answer:

$\alpha + 2 \alpha = - 9 \\ 3 \alpha = - 9 \\ \alpha = - 3 \\ \alpha (2 \alpha ) = m \\ 2 \alpha { }^{2} = m \\ 2(3) {}^{2} = m \\ 2(9) = m \\ m = 18$

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