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.

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Solution

True, since in this case discriminant is always positive, so it has always real roots, i.e. ac < 0 and so $b^{2}$ – 4ac > 0

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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.

Question 2 (ii)
Write whether the given statement is true or false. Justify your answer.
Every quadratic equation has at least one real roots.

Question 2 (iii)
Write whether the given statement is true or false. Justify your answer.
Every quadratic equation has at least two roots.

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Solving a Quadratic Equation by Factorization Method

Standard X Mathematics

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Question 2 (v) Write whether the given statement is true or false. Justify your answer. If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.

True, since in this case discriminant is always positive, so it has always real roots, i.e. ac < 0 and so b2 – 4ac > 0

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.

True, since in this case discriminant is always positive, so it has always real roots, i.e. ac < 0 and so $b^{2}$ – 4ac > 0