Question
Download Solution PDFIf α and β are the roots of the equation 2x2 - 3x - 5 = 0, then the quadratic equation whose roots are
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The roots of equation 2x2 - 3x - 5 = 0 are α and β.
The roots of another equation are
Calculation:
Using the hit and trial method on the given equation to find values of α and β.
2x2 - 3x - 5 = 0
= 2x2 - 5x + 2x - 5
= x(2x - 5) +1(2x - 5)
= (2x - 5)(x + 1)
x =
thus α =
Now solving,
Now,
Quadratic equation whose roots are
(x - (
⇒ (x + 5/2) (x + 2/5) = 0
⇒ x2 + 5x/2 + 2x/5 + 1 = 0
⇒ (10x2 + 25x + 4x + 10)/10 = 0
⇒ 10x2 + 29x + 10 = 0
∴ The correct answer is option (2)Last updated on Jul 18, 2025
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