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If both (x-2)and (x-1/2) are factors …

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If both (x-2)and (x-1/2) are factors of px^2+5x+r, prove that p= r

Posted by Sonali Singh 2 years, 3 months ago

CBSE > Class 09 > Mathematics

2 answers

Sonali Singh 2 years, 2 months ago

Thanks a lot 😃😃😃🫂

Harshita Dashoni 2 years, 3 months ago

The given polynomial is Q(r)=px^2+5x+r It is also given that (x-2) and (x-1/2)are the factor of Q(x) which means that Q (2)=0 and Q(1/2) =0 Let us first substitute Q(2)=0 in Q(x)=px^2+5x+r as shown below : =Q(r)=px^2+5x+r =Q(2)=p(2)^2+5(2)+r = 0=p(4)+10+r = 0=4p+10+r =4p+r=-10 ...........(1) Now substitute Q(1/2)=0in Q(x)=px^2+5x+r as shown below: =Q(x)=px^2+5r+r =Q(1/2)=p(1/2)+5(1/2)+r = 0 =p/4+5/2+r = 0 =p+5(2)+r(4)/4 = 0 =p+10+4r = p+4r= -10 ...........(2) Now subtracting the equations (1) and (2) we get = (4p - p) +(r -4r) = -10+10 = 3p - 3r =0 = 3p = 3r = p = r Hence p = r is proved

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