Question

I. Find the value of p for which root one quadratic equation
px²-14x+8=0 is six times the other
​

Answer 1

Answer:

The value of p is 3

Step-by-step explanation:

Given :

One root of the quadratic equation px² - 14x + 8 = 0 is 6 times the other.

To find :

the value of p

Solution :

Let one root be α

Then the other root = 6α

The given quadratic equation is of the form ax² + bx + c = 0

• a = p
• b = -14
• c = 8

From the relation between roots and coefficients :

Sum of roots = -b/a

Product of roots = c/a

So,

Sum of roots = -b/a

α + 6α = -(-14)/p

 7α = 14/p

  α = 2/p

Product of roots = c/a

 α × 6α = 8/p

  6α² = 8/p

  3α² = 4/p

   3(2/p)² = 4/p

   3(4/p²) = 4/p

   12/p² = 4/p

     12/p = 4

    p = 12/4

    p = 3

Therefore, the value of p is 3