(A) Let $y = x - 2$. The equation becomes $y^2 - 3y + 2 = 0$.Factoring the quadratic equation,we get $(y - 1)(y - 2) = 0$.So,$y = 1$ or $y = 2$.Substi

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(A) Let $y = x - 2$. The equation becomes $y^2 - 3y + 2 = 0$.Factoring the quadratic equation,we get $(y - 1)(y - 2) = 0$.So,$y = 1$ or $y = 2$.Substituting back $x - 2 = y$:Case $1$: $x - 2 = 1 \implies x = 3$.Case $2$: $x - 2 = 2 \implies x = 4$.The roots of the equation are $3$ and $4$.The product of the roots is $3 \times 4 = 12$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

Easy

What is the product of the roots of the equation $(x - 2)^2 - 3(x - 2) + 2 = 0$?

A
$12$
B
$6$
C
$7$
D
$8$

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

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Medium

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DifficultJEE MAIN 2019

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DifficultIIT 1985

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What is the product of the roots of the equation $(x - 2)^2 - 3(x - 2) + 2 = 0$?

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For what set of values of $p$ do the roots of the equation $3x^2 + 2x + p(p - 1) = 0$ have opposite signs?

If $A$ and $G$ represent the arithmetic mean and geometric mean respectively,and $x^2 - 2Ax + G^2 = 0$,then which of the following is true?

The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation $6x^2 - 11x + \alpha = 0$ are rational numbers is:

If $P(x) = ax^2 + bx + c$ and $Q(x) = -ax^2 + dx + c$ where $ac \neq 0$,then $P(x) \cdot Q(x) = 0$ has at least:

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