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Question
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
Solution
Given equation is –2x2 + 3x + 2 = 0
On company with ax2 + bx + c = 0, we get
a = –2, b = 3 and c = 2
∴ Discriminant, D = b2 – 4ac
= (3)2 – 4 – (–2)(2)
= 9 + 16
= 25 > 0
Therefore, the equation –2x2 + 3x + 2 = 0 has two distinct real roots because we know that,
If the equation ax2 + bx + c = 0 has its discriminant greater than zero, then it has two distinct real roots.
Roots, `x = (-b +- sqrt(D))/(2a)`
= `(-3 +- sqrt(25))/(2(-2))`
= `(-3 +- 5)/(-4)`
= `(-3 + 5)/(-4), (-3 - 5)/(-4)`
= `2/(-4), (-8)/(-4)`
= `- 1/2, 2`
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