Question

If p and q are the roots of the equation 2x² - 6x + a = 0 and 2p + 5q= 12 then the value of a will be

Answer 1

Answer:

           a = 4

Step-by-step explanation:

The sum of the roots of a quadratic ax²+bx+c is -b/a, and the product of the roots is c/a.

Since p and q are the roots of 2x²-6x+a,

• pq = a/2  ⇒  a = 2pq

• p + q = 6/2 = 3

Also given

• 2p + 5q = 12

Taking 2 times the p+q equation from the last equation gives

    (2p+5q) - 2(p+q)  =  12 - 2×3

⇒  3q = 6

⇒  q = 2

Then also

  p = 3 - q = 3 - 2 = 1.

Therefore

 a = 2pq = 2×1×2 = 4