Math, asked by rohitmeena25118, 9 months ago

If both (x-2) and (x-1 by 2) are factors of px square + 5x + r, show that p=r. ​

Answers

Answered by Cosmique
7

Question :-

If both (x-2) and ( x-(1/2)) are factors of px²+5x+r , show that p = r .

Solution :-

It is given that two factors of given quadratic polynomial are

x - 2  and x-(1/2)

so,

two zeroes of polynomial will be

x = 2   and   x = 1 / 2

⇨ Putting x = 2 in px²+5x+r we will get zero

   p (2)²+ 5(2) + r = 0

   4 p + 10 + r = 0

   4 p + r = -10  ......eqn(1)

⇨also, on Putting x =1/2 in px²+5x+r we will zero

  p(1/2)² + 5(1/2) + r = 0

  p / 4  + 5 / 2 + r = 0

multiplying by 4 both sides

  p + 10 + 4 r = 0

  p + 4 r = -10   ...... eqn(2)

Using eqn(1) and (2)

→   4 p + r = p + 4 r

→   4 p - p = 4 r - r

→     3 p = 3 r

→ p = r         ( Proved. )

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