find the value of p for which one root of the quadratic equation px2 -14x +8=0 is 6 times the other
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Let first root be α, so second root will be 6α.
Given equation: px^2 - 14x + 8 = 0
which is in the form ax^2 + bx + c = 0
So, sum of roots = -b/a
That is, 7α = 14/p -----1)
And, product of roots = c/a
That is, 6α^2 = 8/p. -----2)
Solving both the equations,
α = 1/6
Putting the value of α in the given equation in the place of x.
So, p = -204
Also, satisfying the value of 6α = 1 in the place of x, p = 6
Given equation: px^2 - 14x + 8 = 0
which is in the form ax^2 + bx + c = 0
So, sum of roots = -b/a
That is, 7α = 14/p -----1)
And, product of roots = c/a
That is, 6α^2 = 8/p. -----2)
Solving both the equations,
α = 1/6
Putting the value of α in the given equation in the place of x.
So, p = -204
Also, satisfying the value of 6α = 1 in the place of x, p = 6
harshitachouksey:
thank you
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