`a x^2 + bx + c = 0` has real roots, `a_1 x^2 + b_1 x + c = 0` has real roots, `a,b,c,a_1,b_1,c_1` are real then roots of `(a + a_1)x^2 + (b + b_1)x + (c-c_1 ) = 0 `are

ax^(2)+bx+c=0 has real roots a_(1)x^(2)+b_(1)x+c=0 has real roots,a,b,c,a_(1),b_(1),c_(1) are real then roots of (a+a_(1))x^(2)+(b+b_(1))x+(c-c_(1))=0 are

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

If a , b , c , are real, then prove that roots of the equation 1/(x-a) + 1/(x-b) + 1/(x-c) = 0 are real.

If one of the roots of the equation ax^2 + bx + c = 0 be reciprocal of one of the a_1 x^2 + b_1 x + c_1 = 0 , then prove that (a a_1-c c_1)^2 =(bc_1-ab_1) (b_1c-a_1 b) .

Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbeta,w h e r ealpha >1 , then show that 1+c/a+|b/a|<0

Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbeta,w h e r ealpha >1 , then show that 1+c/a+|b/a|<0

Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbeta,w h e r ealpha 1 , then show that 1+c/a+|b/a|<0