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प्रश्न
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
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उत्तर
The given quadratic equation is
x2 + 5x + 5 = 0
Here, a = 1, b = 5 and c = 5
Discriminant
= b2 - 4ac
= (5)2 - 4 x 1 x 5
= 25 - 20
= 5 > 0
so the given equation has real roots given by
a = `(-b + sqrt(b^2 - 4ac))/(2a)`
= `(-5 + sqrt(25 - 4 xx 1 xx 5))/(2 xx 1)`
= `(-5 + sqrt(5))/(2)`
and β = `(-b - sqrt(b^2 - 4ac))/(2a)`
= `(-5 -sqrt(25 - 4 xx 1 xx 5))/(2 xx 1)`
= `(-5 - sqrt(5))/(2)`
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Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
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∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
