Question
Form the quadratic equation whose roots are 3 and –2.
The correct answer is
x² – x – 6 = 0
Forming Quadratic Equation from Roots
To form a quadratic equation given its roots, we use the standard form:
$ x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0 $
Given the roots are 3 and –2.
Calculating Sum and Product of Roots
- Sum of roots: $ 3 + (-2) = 3 - 2 = 1 $
- Product of roots: $ 3 \times (-2) = -6 $
Constructing the Quadratic Equation
Substitute the calculated sum and product into the standard form:
$ x^2 - (1)x + (-6) = 0 $
Simplifying the equation gives:
$ x^2 - x - 6 = 0 $
This matches option B.
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Important Questions from Quadratic equation
What number should be subtracted from x3−4x2−8x+11 to make the number divisible by (x+2)?
- Find the value of K if the quadratic equations $2x^2 + Kx + 8 = 0$ and $3x^2 + 4x + 12 = 0$ have both roots common.
- If sum and product of the roots of a quadratic equation are $(4-3\sqrt{2})$ and -28, respectively, then find the quadratic equation.
- If the quadratic equations $4x^2 + bx + 3 = 0$ and $8x^2 + 4x + c = 0$ have both the roots common, find the values for b and c, respectively.
- Determine the nature of the roots of the quadratic equation $3x^2 + 2x + 5 = 0$.
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