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Nature of Roots

if f(x)=ax^2+...

Question

if f(x)=ax^2+bx+c, g(x)= -ax^2 +bx+ c where ac not equal to zero then prove that f(x).g(x)=0 has at least two real root.

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Similar questions

P (x) = {a x}^{2} + b x + c

Q (x) = - {a x}^{2} + b x + c

a c \neq 0

, then show that

P (x) Q (x)

=0 has at least two real roots.

Q. If the parabola represented by f(x) = ax² + bx + c cuts x-axis at two distinct points, then the polynomial ax² + bx + c has ________ real zeroes.

Q. Consider two quadratic expressions

f (x) = a x^{2} + b x + c

g (x) = a x^{2} + p x + q

(b \neq q)

such that their discriminants are equal. If

f (x) = g (x)

x = α

f (x) = a x^{2} + b x + c

has no real zeros and

a + b + c < 0

f (x) = a x^{2} + b x + c

has no real zeroes and

a + b + c < 0

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