If `f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,w h e r ea c!=0,` then prove that `f(x)g(x)=0` has at least two real roots.

If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac !=0, then prove that f(x)g(x)=0 has at least two real roots.

If f(x)=ax^(2)+bx+c,g(x)=-ax^(2)+bx+c, where ac !=0 then prove that f(x)g(x)=0 has at least two real roots.

True or false The equation 2x^2+3x+1=0 has an irrational root. If a

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

Let f(x) = x^2 + b_1x + c_1 . g(x) = x^2 + b_2x + c_2 . Real roots of f(x) = 0 be alpha, beta and real roots of g(x) = 0 be alpha+gamma, beta+gamma . Least values of f(x) be - 1/4 Least value of g(x) occurs at x=7/2

Let f(x) = x2 + b_1x + c_1. g(x) = x^2 + b_2x + c_2 . Real roots of f(x) = 0 be alpha, beta and real roots of g(x) = 0 be alpha+gamma, beta+gamma . Least values of f(x) be - 1/4 Least value of g(x) occurs at x=7/2

Let f(x) = x2 + b_1x + c_1. g(x) = x^2 + b_2x + c_2 . Real roots of f(x) = 0 be alpha, beta and real roots of g(x) = 0 be alpha+gamma, beta+gamma . Least values of f(x) be - 1/4 Least value of g(x) occurs at x=7/2

Let f(x) = x2 + b_1x + c_1. g(x) = x^2 + b_2x + c_2 . Real roots of f(x) = 0 be alpha, beta and real roots of g(x) = 0 be alpha+gamma, beta+gamma . Least values of f(x) be - 1/4 Least value of g(x) occurs at x=7/2