Question

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

Answer 1

Answer:

p = -5, q = -6

Step-by-step explanation:

2x²-5x-3 = 2x²-6x+x-3

              = 2x(x-3)+1(x-3)

              = (x-3)(2x+1)

Hence, the zeros of 2x²-5x-3 are -1/2 and 3.

Zeros of the polynomial x²+px+q  are double in value to -1/2 and 3,

Thus zeros are -1 and 6.

Now, quadratic expression with zeros -1 and 6 is given by

(x + 1)(x-6) = x²-5x-6. By comparison, p = -5 and q = -6.

Answer 2

Answer:

p=5 & q=-6

Step-by-step explanation:

2x

2

−5x−3=0

2x

2

−6x+x−3=0

(x−3)(2x+1)=0

x=3,−

2

1

Now,

Zeroes of the polynomial x

2

−px+q are double in values to the zeroes of polynomial 2x

2

−5x−3.

Therefore,

Zeroes of polynomial x

2

−px+q will be- 6,−1

Therefore,

Sum of roots =

a

−b

6+(−1)=−(−p)

⇒p=5

Product of root =

a

c

6×−1=q

⇒q=−6

Hence the values of p and q are 5 and −6 respectively.