Question

If p, q are the roots of the equation$x^2-3x+2=0$, find the equation which has roots as (2p + 1) and (2q + 1).

• A. x² – 7x + 15 = 0
• B. x² – 8x + 12 = 0
• C. 2x² – 8x + 15 =0
• D. 2x² – 7x + 14 = 0
• E. x² – 8x + 15 = 0

Answer 1

The correct option is E x² – 8x + 15 = 0

Soln:

Given equation:$x^2-3x+2=0$with roots p, q

When the roots become 2p and 2q, the equation becomes:${\left(\frac{x}{2}\right)}^2-3\left(\frac{x}{2}\right)+2=0,x^2-6x+8=0$

When the roots become$(2p+1)\&(2q+1)$the equation becomes:

$(x-1{)}^2-6(x-1)+8=0,x^2-8x+15=0$. Hence option (e)