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Quadratic Equation

The value of ...

Question

The value of $a$ for which the equation $(a^{2} - a - 2) x^{2} + (a^{2} - 4) x + (a^{2} - 3 a + 2) = 0$ have more than two roots

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Solution

The correct option is C $2$
Since, the given equation have more than two roots so this is identity.

Thus given equation is satisfied for all values of $x$ , so all the coeffients must be zero. Then,
$a^{2} - a - 2 = 0 \Rightarrow a = - 1, 2$
$a^{2} - 4 = 0 \Rightarrow a = - 2, 2$
$a^{2} - 3 a + 2 = 0 \Rightarrow a = 1, 2$
Therefore, the common value of $a = 2$

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Quadratic Equation

Standard XII Mathematics

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The value of a for which the equation (a2−a−2)x2+(a2−4)x+(a2−3a+2)=0 have more than two roots

The correct option is C 2Since, the given equation have more than two roots so this is identity. Thus given equation is satisfied for all values of x, so all the coeffients must be zero. Then, a2−a−2=0⇒a=−1,2 a2−4=0⇒a=−2,2 a2−3a+2=0⇒a=1,2 Therefore, the common value of a=2

The value of $a$ for which the equation $(a^{2} - a - 2) x^{2} + (a^{2} - 4) x + (a^{2} - 3 a + 2) = 0$ have more than two roots