Any quadratic equation will have two roots. Justify.

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Solution

A quadratic equation is an equation involving maxiumum power of x to be 2 and also involves other x terms and may be a constant term.
For example: $x^{2} + 4 x + 6 = 0$ is a quadratic equation.
Let us take (x - 3)(x + 4) = 0, which when expanded gives you $x^{2} + x - 12 = 0$ ..... (1)
So, either $x - 3 = 0$ or $x + 4 = 0 \to x = 3 o r x = - 4$ which are called roots of equation $x^{2} + x - 12 = 0 \dots$
Now, let us take another equation (x - 3)(x - 5) = 0, which when expanded becomes $x^{2} - 8 x + 15 = 0$ ....(2)
Its roots are $x - 3 = 0$ or $x - 5 = 0 \to x = 3 o r x = 5$ .
So, we have two equations where we have a common root x = 3.
Hence, a common root between two quadratic equations is a root which is common to both.

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

Question 3
Does a quadratic equation with integral coefficient has integral roots. Justify your answer.

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