Write whether the statement are true or false. Justify your answer.
Every quadratic equation has exactly one root.
(x2 + 1)2 – x2 = 0 has
(A) four real roots (B) two real roots
(C) no real roots (D) one real root.
Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is
(A) 0 only (B) 4 (C) 8 only (D) 0, 8
If 1/2 is a root of the equation x2 +kx – 5/4 = 0, then the value of k is
1 (A) 2 (B) – 2 (C) 1/4(D)1/2
Which of the following equations has 2 as a root?
(A) x2 – 4x + 5 = 0 (B) x2 + 3x – 12 = 0 (C) 2x2 – 7x + 6 = 0 (D) 3x2 – 6x – 2 = 0
Which one of the following is not a quadratic equation?
(A) (x + 2)2 = 2(x + 3)
(B) x2 + 3x = (–1) (1 – 3x)2
(C) (x + 2) (x – 1) = x2 – 2x – 3
(D) x3 – x2 + 2x + 1 = (x + 1)3
Vijay had some bananas, and he divided them into two lots A and B. He sold the first lot at the rate of Rs 2 for 3 bananas and the second lot at the rate of Re 1 per banana, and got a total of Rs 400. If he had sold the first lot at the rate of Re 1 per banana, and the second lot at the rate of Rs 4 for 5 bananas, his total collection would have been Rs 460. Find the total number of bananas he had.
Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received Rs 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs 20 more as annual interest. How much money did she invest in each scheme?
A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby, getting a sum Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.
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