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Question
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
Solution
Given equation is, `x^2 + 9sqrt(3)x + 24 = 0`
Comparing the given equation with ax2 + bx + c = 0, we get
a = 1, b = `9sqrt(3)`, c = 24
Discriminant, D = b2 – 4ac
= `(9sqrt(3))^2 - 4(1)(24)`
= 243 – 96
= 147
Here, D > 0.
As a result, the roots of the quadratic equation are both real and unequal.
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