Mathematics
Determine whether the following quadratic equation has real roots.
5š„2 ā 9š„ + 4 = 0
(a) Give reasons for your answer.
(b) If the equation has real roots, identify them.
Quadratic Equations
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Answer
(a) Given, equation : 5š„2 ā 9š„ + 4 = 0
Comparing above equation with ax2 + bx + c = 0, we get :
a = 5, b = -9 and c = 4.
Discriminant (D) = b2 - 4ac = (-9)2 - 4 Ć 5 Ć 4 = 81 - 80 = 1.
Since, D > 0 and a perfect square.
Hence, equation 5š„2 ā 9š„ + 4 = 0 has real roots.
(b) Solving,
ā 5š„2 ā 9š„ + 4 = 0
ā 5x2 - 5x - 4x + 4 = 0
ā 5x(x - 1) - 4(x - 1) = 0
ā (5x - 4)(x - 1) = 0
ā 5x - 4 = 0 or x - 1 = 0
ā 5x = 4 or x = 1
ā x = or x = 1.
Hence, roots of the equation are 1 and .
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