Question

can any1 solve this plzz

Answer 1

Solution:

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Given:

px² + 14x + 8 = 0,

one root of this equation is 6 times the other.

α = 6β
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To find :

The value of p.

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We know that,

The equation is of the form,

ax² + bx + c = 0,

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here,

a = p

b = -14

c = 8,.

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We know that,

Sum of the zeroes = $\frac{-b}{a}$

=> α + β = $\frac{-(-14)}{p}$

=> 6β + β =$\frac{14}{p}$

=> 7β = $\frac{14}{p}$

=> ∴ β = $\frac{2}{p}$

=> α = $6( \frac{2}{p} )$

=> ∴ α = $\frac{12}{p}$

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We know that,

Product of the zeroes = $\frac{c}{a}$

=> αβ = $\frac{8}{p}$

=> (6β)(β) = $\frac{8}{p}$

=> $( \frac{12}{p} )( \frac{2}{p} )$ = $\frac{8}{p}$

=> $\frac{24}{p^2} = \frac{8}{p}$

=> $24p = 8p^2$

=> $24 = 8p$

=> ∴ p = 3

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                             Hope it Helps!!