Q) If X = and X = − 3 are the roots of the equation aX2 + 7X + b = 0, find the values of a and b. Ans: We know that if a and b are the roots of a polynomial, then the polynomial can be given by (X – a) (X – b) […]
If x=2/3 and x=−3 are the roots of the equation, ax2+7x+b=0, find the values of a and b. Read More »
Q) The graph of the polynomial – ax²+bx+c is shown below. Write the signs of ‘a’ and ‘b² – 4ac’. Ans: Clearly, f(x) = ax² + bx + c represent a parabola opening upwards. Therefore, a>0 Since, the parabola cuts the x-axis at two points, this means that the polynomial will have two real solutions. Hence,
Q) Find the value of m for which the quadratic equation (m + 1) y2 – 6(m+1) y + 3(m+9) = 0, m ≠ -1 has equal roots. Hence find the roots of the equation. [CBSE, Sample Question Paper – Standard – 2024] Ans: Given quadratic equation is: (m
Find the value of m for which the quadratic equation (m + 1) y2 – 6(m+1) y + 3(m+9)= 0 Read More »
Q) If 𝛼, β are zeroes of quadratic polynomial x2 – 2x + 3, find the polynomial whose roots are:1. 𝛼 + 2, 𝛽 + 22. Ans: Given polynomial equation x2 – 2x + 3 = 0 Comparing with standard polynomial, ax2 + b x + c = 0, we get, a = 1, b =
Q) Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km. 1. What
Raj and Ajay are very close friends. Both the families decide to go to Read More »
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
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