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Question
Find whether the following equation have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0
Solution
Given equation is 8x2 + 2x – 3 = 0
On comparing with ax2 + bx + c = 0, we get
a = 8, b = 2 and c = – 3
∴ Discriminant, D = b2 – 4ac
= (2)2 – 4(8)(– 3)
= 4 + 96
= 100 > 0
Therefore, the equation 8x2 + 2x – 3 = 0 has two distinct real roots because we know that,
If the equation ax2 + bx – c = 0 has discriminant greater than zero, then it has two distinct real roots.
Roots, `x = (-b +- sqrt(D))/(2a)`
= `(-2 +- sqrt(100))/16`
= `(-2 +- 10)/16`
= `(-2 + 10)/16, (-1 - 10)/16`
= `8/16, -12/16`
= `1/2, - 3/4`
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