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ICSE Class 10 Mathematics Question 12 of 21

Solved 2024 Question Paper ICSE Class 10 Mathematics — Question 6

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6
Question

Question 6(i)

Solve the following quadratic equation for x and give your answer correct to three significant figures :

2x2 - 10x + 5 = 0

Answer

Comparing equation 2x2 - 10x + 5 = 0 with ax2 + bx + c = 0, we get :

a = 2, b = -10 and c = 5

By formula,

⇒ x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting values we get :

⇒x=−(−10)±(−10)2−4×2×52×2=10±100−404=10±604=10±2154=2(5±15)4=5±152=5±3.872=5+3.872,5−3.872=8.872,1.132=4.44,0.565\Rightarrow x = \dfrac{-(-10) \pm \sqrt{(-10)^2 - 4 \times 2 \times 5}}{2 \times 2} \\[1em] = \dfrac{10 \pm \sqrt{100 - 40}}{4} \\[1em] = \dfrac{10 \pm \sqrt{60}}{4} \\[1em] = \dfrac{10 \pm 2\sqrt{15}}{4} \\[1em] = \dfrac{2(5 \pm \sqrt{15})}{4} \\[1em] = \dfrac{5 \pm \sqrt{15}}{2} \\[1em] = \dfrac{5 \pm 3.87}{2} \\[1em] = \dfrac{5 + 3.87}{2}, \dfrac{5 - 3.87}{2} \\[1em] = \dfrac{8.87}{2}, \dfrac{1.13}{2} \\[1em] = 4.44, 0.565

Hence, x = 4.44, 0.565