Quadratic Equations Exam Prep
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Quadratic equations
Sample questions with model answers
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Explain how to complete the square for the equation $x^2 + 6x + 5 = 0$.
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To complete the square, rewrite as $(x + 3)^2 - 4 = 0$, then solve for $x$.
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Solve the quadratic equation $2x^2 - 8x + 6 = 0$ using the quadratic formula.
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Using the quadratic formula, the roots are $x = 3 \pm \sqrt{3}$.
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The ratio of the interest received when Rs. (x + 500) is invested at 32% p.a. simple interest for 4 years to the interest received when Rs. (x - 500) is invested at 20% p.a. compound interest, compounded annually for 2 years, is 64 : 11. Find the value of 'x'.
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x = Rs. 1,500
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Three friends, Anya, Bhavya, and Chitra, decide to launch a boutique specializing in Anarkali suits. They initially invest capital in the ratio 3 : 4 : 6. After six months of successful sales, Anya confidently increases her investment by 40%. Simultaneously, Bhavya withdraws 1/4 of her initial capital for personal travel, while Chitra leaves her investment entirely untouched. At the end of the first year of operation, the boutique generates a total profit of Rs. 36,000. What is Bhavya's exact share of this annual profit?
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Bhavya's share = Rs. 9,618.32
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