If the roots x1 and x2 of the quadratic equation x2 - 2x + c = 0 also satisfy the - Maths - Quadratic Equations

Question

If the roots x1 and x2 of the quadratic equation x2 - 2x + c = 0
also satisfy the equation 7x1 – 4x2 = 47, find the roots and
hence find the value of c

Lalit Mehra · Accepted Answer

x1 and x2 are the roots of x2-2x+c=0
∴ x1+x2=2      
1x1x2=c           
2Given:7x1-4x2=47      
3Solving 1 and 3, we get7x1-4x2=474x1+4x2=811x1=55⇒x1=5511=5∴ 5+x2=2⇒x2=2-5=-3∴c=x1x2=5×-3=-15

If the roots x1 and x2 of the quadratic equation x2 - 2x + c = 0 also satisfy the equation 7x1 – 4x2 = 47, find the roots and hence find the value of c.