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