Q) Two water taps together can fill a tank in 9 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time (in hrs) which each tap can separately fill the tank. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION It is given that,Time taken […]
polynomials
Q) A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION It is given that, Speed of motor boat = 18 km/hrDistance travelled =24
Q) If 𝛼, β are zeroes of quadratic polynomial 5×2 + 5x + 1, find the value of1. 𝛼2 + 𝛽22. 𝛼‾1 + 𝛽‾1 Ans: Given polynomial equation 5×2 + 5x + 1 = 0 The roots of the polynomial be α and β. We know that sum of roots (α + β) = α + β
Q) In a pool at an aquarium, a dolphin jumps out of the water travelling at 20 cm per second. Its height above water level after t seconds is given by: h = 20t – 16t2. Based on the above, answer the following questions:(i) Find zeroes of polynomial p(t) = 20t – 16t².(ii) Which of
Q) Find the value of ‘p’ for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other. Ans: Let one the roots be then by the given condition, other root is 6 We know that sum of roots (α + β) = Sum of roots
Q) Find the discriminant of the quadratic equation 4×2 – 5 = 0 and hence comment on the nature of the equation. Ans: Given equation is 4×2 – 5 = 0 or we can say that, Find the discriminant of 4×2 + 0x – 5 = 0 Let’s compare it with standard quadratic equation ax2 +b
Q) Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots. Ans: Given quadratic equation is: px (x – 2) + 6 = 0 or we can rewrite it as, px2 – 2p x + 6 = 0 In this equation, we can
Q) Find the sum and product of the roots of the quadratic equation 2×2 – 9x + 4 = 0. Ans: We know that sum of roots (α + β) = Sum of roots = = Next, we know that the product of the roots (α x β) = Product of the roots
Find the sum and product of the roots of the quadratic equation 2x^2 – 9 x + 4 = 0. Read More »
Q) If one zero of the polynomial p(x) = 6×2 + 37 x – (k-2) is reciprocal of the other, then find the value of k. Ans: Let’s consider the one zero of the given polynomial be , then other zero will be . We know that Product of the zeroes (α x β) =