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Byju's Answer

Standard XI

Mathematics

Common Roots

If the equati...

Question

If the equation $x^{2} + p x + q = 0$ and $x^{2} + q x + p = 0$ , have a common root, then p + q + 1 =

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Solution

The correct option is A
0

Let α is the common root, so $α^{2} + p α + q = 0$

and $α^{2} + q α + p = 0$

⇒ (p - q) α + (q - p) = 0 ⇒ α=1

Put the value of α , p + q + 1 = 0

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If the equation x2+px+q=0 and x2+qx+p=0, have a common root, then p + q + 1 =

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If the equation $x^{2} + p x + q = 0$ and $x^{2} + q x + p = 0$ , have a common root, then p + q + 1 =

The correct option is A
0

Let α is the common root, so $α^{2} + p α + q = 0$

and $α^{2} + q α + p = 0$

⇒ (p - q) α + (q - p) = 0 ⇒ α=1

Put the value of α , p + q + 1 = 0