Question

If a(5+q²)+2bq+c=0 and a(5+r²)+2bq+c =0 where a≠0 then q+r=​

Answer 1

Answer:

Consider the quadratic equation a(p+x)2+2bpx+c=0 this has two roots and given that q,r satisfy the equation implies q,r are the roots of this equation. Rewriting the equation as ax2+2px(a+b)+(c+ap2)=0 the product of the roots qr is given by constant term divided by coefficient of x2 .

∴qr=c+ap2a

Answer 2

Answer:

if p and q be the roots of the given quadratic equation then, a(5+r^2) + 2br + c = 0 and a(5+q^2) + 2bq + c = 0

so, consider the equation

a(5+x^2) + 2bx + c = 0

whose roots are q and r

then we write that as

ax^2 + 2bx + a + c = 0

where q + r = -2b/a