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Question
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
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Solution
The quadratic formula for finding the roots of quadratic equation
ax2 + bx + c = 0, a ≠ 0 is given by,
x = `(-b +- sqrt(b^2 - 4ac))/(2a)`
∴ x = `(-7 +- sqrt((-7)^2 - 4(-1)(-10)))/(2(-1))`
= `(-7 +- sqrt(9))/(-2)`
= `(7 +- 3)/2`
= 5, 2
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Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
