If roots of x² - 9x + 20 = 0 are increased by 1, new equation is?
- x² - 13x + 30 = 0
- x² - 12x + 30 = 0
- x² - 11x + 30 = 0
- None of these
Explanation
If roots of x² - 9x + 20 = 0 are increased by 1, the new equation is x² - 11x + 30 = 0
Solution:
Step 1: Find the roots of x² - 9x + 20 = 0
Factorize:
x² - 9x + 20 = 0
x² - 5x - 4x + 20 = 0
x(x - 5) - 4(x - 5) = 0
(x - 4)(x - 5) = 0
So the roots are x = 4 and x = 5
Step 2: Increase each root by 1
New roots = 4 + 1 = 5 and 5 + 1 = 6
Step 3: Form the new equation
If roots are α and β, then equation is x² - (α + β)x + αβ = 0
Here α = 5, β = 6
Sum of roots = 5 + 6 = 11
Product of roots = 5 * 6 = 30
Therefore, new equation is:
x² - 11x + 30 = 0
Last verified on 24-05-2026
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