Question

if the zeros of polynomial x²+px+q are double in value of the zeros of 2x²-5x-3 respectively find the values of p and q

Answer 1

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Answer 2

Hii friend,

=> (2X²-5X+3)

=> 2X²-6X+X+3

=> 2X(X-3) +1(X+3)

=> (X-3) (2X+1)

=> (X-3) = 0 OR (2X+1) = 0

=> X = 3 OR X = -1/2

According to question,

The zeros of the polynomial X²+PX+Q is double in the Value of the zeros of the polynomial 2X²-5X-3.

zero's of the polynomial 2X²-5X-3 is 3 and -1/2

And, the zeros of the polynomial X²+PX+Q are 2 × 3= 6 and 2 × -1/2 = -1

Sum of zeros = (Alpha+ Beta) = -B/A

{6+(-1)} = -P/1

6-1 = -P/1

-P = 5

P= -5

and,

Product of zeros = C/A

6 × (-1) = Q/1

-6 = Q

Q = -6

Hence,

P = -5 and Q = -6

HOPE IT WILL HELP YOU..... :-)