Question

One root of px2 – 14x + 8 = 0 is six times the other then p is:
A) 0
B) 3
C) 1/3
D) 1

Answer 1

Let one of the roots be a

Other root would be:6a

The equation is px² -14x +8=0

Here,

a=p,b= -14 and c=8

Now,

★Product of roots(c/a)

6a.a= (8/p)

→6a²=8/p

→p=8/6a².............(1)

★Sum of zeros(-b/a)

6a+a=-(-14)/p

→7a=14/p

→p=2/a.................(2)

From (1) and (2),

$\sf{ \frac{2}{a} = \frac{8}{6a {}^{2} } } \\ \\ \implies \: \sf{12a {}^{2} = 8a } \\ \\ \implies \: \sf{3a = 2} \\ \\ \implies \: \huge{ \sf{a = \frac{2}{3} }}$

•Putting a=2/3 in (2),

p=2/(2/3)

→p= 3

Thus,the correct option is (b)