If the equations k (6 x 2+3)+ rx +2 x 2-1=0 and 6 k (2 x 2-1)+ px +4 x 2+2=0 have both roots common, then the value of (2 r-p) is :

Question

If the equations k (6 x 2+3)+ rx +2 x 2-1=0 and 6 k (2 x 2-1)+ px +4 x 2+2=0 have both roots common, then the value of (2 r-p) is : (A) 0 (B) 1 / 2 (C) 1 (D) None of these

Tardigrade Admin · Accepted Answer

Given equations are k(6 x2+3)+r x+2 x2-1=0 and 6 k(2 x2-1)+p x+4 x2+2=0 ⇒ (6 k+2) x2+r x+3 k-1=0 dots(i) ⇒ (12 k +4) x 2+ px -6 k +2=0 ldots( ii ) Let α and β be the roots of both equations (i) and (ii). ∴ α+β=(- r /6 k +2) (from (i)) and α+β=(-p/12 k+4) (from(ii)) ∴ (- r /2(1+3 k ))=(- p /4(1+3 k )) ⇒ (- r /2)=(- p /4) ⇒ -2 r=-p ⇒ 2 r-p=0

Q. If the equations k(6x2+3)+rx+2x2−1=0 and 6k(2x2−1)+px+4x2+2=0 have both roots common, then the value of (2r−p) is :

0

1 / 2

1

None of these

Q. If the equations $k (6 x^{2} + 3) + r x + 2 x^{2} - 1 = 0$ and $6 k (2 x^{2} - 1) + p x + 4 x^{2} + 2 = 0$ have both roots common, then the value of $(2 r - p)$ is :