Question

Find the value of ‘p’ for which one root of the quadratic equation Px²-14x+8 =0 is 6 times the other.

Answer 1

Heya!
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♦Quadratic Equation ♦
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▪Let the roots be @ and 6@ respectively !


=> We know the relationship between zeroes and Coefficients :


▪Sum of Zeroes = -b/a


=> @ + 6@ = 14/p

=>7@ = 14/ p


=> @ = 2/p.............(1 )


▪Product of Zeroes = c/a

=> @ × 6@ = 8/p

=>6@² = 8/p.............(2)



♦Put @ = 2/p in (2)


=> 6 (2/p)² = 8/p

=>24p = 8p²

=> p = 3



▪Hence the Value of p is 3 .


✔Verification
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Put p = 3


=> 3x² - 14x + 8 = 0

=> 3x² -2x - 12x + 8 = 0

=> x ( 3x - 2 ) -4 ( 3x - 2 )

=> ( 3x - 2 ) ( x - 4 )


▪Roots are x = 4 , 2/3 ✔


▪Here , 4 is six times of 2/3 .



✔Verified !!.
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⚪Hence p => 3 ✔✔

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