Which is the correct pair of roots of x^2+3x-18=0?
Answer and explanation
Correct answer: 3 और -6
The governing concept is factorisation of a quadratic. For x^2+3x−18, we need two numbers whose product is −18 and whose sum is 3, because the constant term is −18 and the coefficient of x is 3. The required numbers are 6 and −3. Thus x^2+3x−18=(x+6)(x−3). Setting each factor equal to zero gives x=−6 and x=3, so the root pair is 3 and −6 and option A is correct. Option B reverses the signs and would correspond to factors (x−3)(x+6) only if the listed values were 3 and −6, not −3 and 6. The pairs in C and D have products −18, but their sums are −7 and 7 respectively, not 3; hence they cannot satisfy the equation.
Frequently asked questions
What is the correct answer to this question?
3 और -6
Why is this the correct answer?
The governing concept is factorisation of a quadratic. For x^2+3x−18, we need two numbers whose product is −18 and whose sum is 3, because the constant term is −18 and the coefficient of x is 3. The required numbers are 6 and −3. Thus x^2+3x−18=(x+6)(x−3). Setting each factor equal to zero gives x=−6 and x=3, so the root pair is 3 and −6 and option A is correct. Option B reverses the signs and would correspond to factors (x−3)(x+6) only if the listed values were 3 and −6, not −3 and 6. The pairs in C and D have products −18, but their sums are −7 and 7 respectively, not 3; hence they cannot satisfy the equation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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