Question

prove that if the coefficient of x square and the constant term of an quadratic equation has opposite signs then the quadratic equation has real roots ​

Answer 1

Answer:

If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots. (vi) If the coefficient of x2and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real ro

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Answer 2

Answer:

Nature of roots of a quadratic equation is dermined by its determinant D which is given by

D = b^2 - 4ac

for real roots D must be greater than or equal to zero.

If coefficient of x^2 and constant term have opposite signs then

if a= a, c= -c or vice versa

then

D = b^2 - 4*a*(-c)

= b^2 + 4ac

now b^2 is always positive whether b is positive or not and 4ac is also positive because of opposite signs of a and c.

Hence, D >=0

and roots are real.