if the coefficient ofx² and the constant terms of the quadratic equation have opposite signs, then the equation has real roots. State true or false and justify.

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Solution

$In quadratic equation, {ax}^{2} + bx + c = 0 Now, when D = b^{2} - 4 ac, here if a and c have opposite sign then ac = - ve and hence - 4 ac = + ev So D = + ve so roots are real .$

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Question 2 (v)
Write whether the given statement is true or false. Justify your answer.
If the coefficient of $x^{2}$ and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

Question 2 (vi)
Write whether the given statement is true or false. Justify your answer.
If the coefficient of $x^{2}$ and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

Write whether the following statemensst are true or false .Justify your answers :

1.Every quadratic equation has at least one real root

2.If in a quadratic equation of ,the coeffecient of x is zero then the quadratic equation has no real roots .

3.If the coeffecient of x2 and the constant term of the quadratic equation have opposite signs ,then the quadratic equation has real roots .

4.A quadratic equation with integeral coeffecient has integral roots.

Q. If the coefficient of x² and the constant term of a quadratic equation have opposite signs, then the roots of the quadratic equation are
______ and _______.

Q. If the coefficient of x² and the constant term of a quadratic equation have the same sign and if the coefficient of x term is zero, then the quadratic equation has ________ roots.

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if the coefficient ofx2 and the constant terms of the quadratic equation have opposite signs, then the equation has real roots. State true or false and justify.

In quadratic equation, ax2+bx+c=0 Now, when D = b2-4ac , here if a and c have opposite sign then ac = -ve and hence -4ac= +evSo D = +ve so roots are real.

if the coefficient ofx² and the constant terms of the quadratic equation have opposite signs, then the equation has real roots. State true or false and justify.

$In quadratic equation, {ax}^{2} + bx + c = 0 Now, when D = b^{2} - 4 ac, here if a and c have opposite sign then ac = - ve and hence - 4 ac = + ev So D = + ve so roots are real .$