The sum of the roots of the following equations is $3$ , and product of the roots of the equation be $2$ . Which one is the equation

x^{2} - 3 x + 2 = 0

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x^{2} + 3 x + 2 = 0

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3 x^{2} + 6 x + 10 = 0

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x^{2} + 3 x - 2 = 0

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Solution

The correct option is A $x^{2} - 3 x + 2 = 0$
Let $a, b$ be the roots of the equation.
Then by the problem,
$a + b = 3$ .......(1) and $a b = 2$ ......(2).
Then the quadratic equation whose roots are $a, b$ be,
$x^{2} - (a + b) x + a b = 0$
or, $x^{2} - 3 x + 2 = 0$ .[ Using (1) and (2)]

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The sum of the roots of the following equations is 3, and product of the roots of the equation be 2. Which one is the equation

The correct option is A x2−3x+2=0Let a,b be the roots of the equation.Then by the problem,a+b=3.......(1) and ab=2......(2).Then the quadratic equation whose roots are a,b be, x2−(a+b)x+ab=0or, x2−3x+2=0.[ Using (1) and (2)]

The sum of the roots of the following equations is $3$ , and product of the roots of the equation be $2$ . Which one is the equation

The correct option is A $x^{2} - 3 x + 2 = 0$
Let $a, b$ be the roots of the equation.
Then by the problem,
$a + b = 3$ .......(1) and $a b = 2$ ......(2).
Then the quadratic equation whose roots are $a, b$ be,
$x^{2} - (a + b) x + a b = 0$
or, $x^{2} - 3 x + 2 = 0$ .[ Using (1) and (2)]