Question

find the value of p for which one root of the quadratic equation is px2 -14x+ 8= 0 is y times the other

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Answer 1

Answer:

p,(X=-2)

14(-2)+8=0

-34+8=0

26=0

p=-26

Answer 2

The value of p for the given quadratic equation is 3

Step-by-step explanation:

Given as :

The quadratic equation

p x² - 14 x + 8 = 0

Let The roots of equation = m , n

According to question

One roots = 6 time the other

First roots = m

Second roots = n = 6 m

Now

The standard quadratic equation is a x² + b x + c = 0

Sum of roots = m + n = $\dfrac{-b}{a}$

Or,                  m + 6 m = $\dfrac{-b}{a}$

Or,                          7 m = $\dfrac{-b}{a}$

Product of roots =  m n = $\dfrac{c}{a}$

i.e                       m × 6 m = $\dfrac{c}{a}$

Or,                             m² = $\dfrac{c}{6a}$

Comparing with equation p x² - 14 x + 8 = 0

So, sum of roots = 7 m = $\dfrac{14}{p}$

Or,                             m = $\dfrac{14}{7p}$  = $\dfrac{2}{p}$                        ..........1

And product of roots = m² = $\dfrac{8}{6p}$ = $\dfrac{4}{3p}$  .              ...........2

Now, From eq 1 and eq 2

( $\dfrac{2}{p}$ )²   = $\dfrac{4}{3p}$  

By cross multiplication

4 × 3 p = 4 × p²

Or,   12 p = 4 × p²

Or,  p = $\dfrac{12}{4}$

∴     p = 3

So, The value of p = 3

Hence, The value of p for the given quadratic equation is 3  . Answer