If the equation x2-px-q-0 and x2-qx-p-0- have a common root- where p q- then find the value of p - q - 1-

Let nbsp;α is the common root, so nbsp;α^2 + pα+q=0 and nbsp;α^2+qα+p=0 subtracting both the equation we get ⇒ (p q) nbsp;α + (q p) = 0 ⇒ nbsp;α 1=0 ...

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Standard XII

Mathematics

Quadratic Equations with Exactly One Root Common

If the equati...

Question

If the equation $x^{2} + p x + q = 0$ and $x^{2} + q x + p = 0,$ have a common root, where $p \neq q,$ then find the value of $p + q + 1 ?$

$0$

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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 $α^{2} + q α + p = 0$
subtracting both the equation we get

$\Rightarrow (p - q) α + (q - p) = 0 \Rightarrow α - 1 = 0 \Rightarrow α = 1$

Put the value of $α = 1$ we get, $p + q + 1 = 0$

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If the equation x2+px+q=0 and x2+qx+p=0, have a common root, where p≠q, then find the value of p+q+1?

The correct option is A 0 Let α is the common root, so α2+pα+q=0 and α2+qα+p=0 subtracting both the equation we get ⇒(p−q)α+(q−p)=0⇒α−1=0⇒α=1 Put the value of α=1 we get,p+q+1=0

If the equation $x^{2} + p x + q = 0$ and $x^{2} + q x + p = 0,$ have a common root, where $p \neq q,$ then find the value of $p + q + 1 ?$

The correct option is A
$0$

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

and $α^{2} + q α + p = 0$
subtracting both the equation we get

$\Rightarrow (p - q) α + (q - p) = 0 \Rightarrow α - 1 = 0 \Rightarrow α = 1$

Put the value of $α = 1$ we get, $p + q + 1 = 0$