Polynomials Important Questions The graph of the polynomial = ax2+bx+c is shown below. Write the signs of ‘a’ and ‘b2-4ac’ Read More » Find the value of m for which the quadratic equation (m + 1) y2 – 6(m+1) y + 3(m+9)= 0, has equal roots. Hence find the roots of the equation. Read More » If 𝛼, β are zeroes of quadratic polynomial x 2 – 2x + 3, find the polynomial whose roots are 1. 𝛼 + 2, 𝛽 + 2 2. (𝛼-1)/(𝛼+1), (𝛽-1)/(𝛽+1) Read More » 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. Read More » Two water taps together can fill a tank in 9 3/8 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. Read More » 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. Read More » If 𝛼, β are zeroes of quadratic polynomial 5x 2 + 5x + 1, find the value of 1. 𝛼2 + 𝛽2 2. 𝛼-1 + 𝛽-1 Read More » 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 the following types of graph represents p(t)? Read More » Find the value of ‘p’ for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other. Read More » Find the discriminant of the quadratic equation 4x^2 – 5 = 0 and hence comment on the nature of the equation. Read More » Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots. Read More » Find the sum and product of the roots of the quadratic equation 2x^2 – 9 x + 4 = 0. Read More » If one zero of the polynomial p(x) = 6x^2 + 37 x – (k-2) is reciprocal of the other, then find the value of k. Read More »

The graph of the polynomial = ax2+bx+c is shown below. Write the signs of ‘a’ and ‘b2-4ac’ Read More »

Find the value of m for which the quadratic equation (m + 1) y2 – 6(m+1) y + 3(m+9)= 0, has equal roots. Hence find the roots of the equation. Read More »

If 𝛼, β are zeroes of quadratic polynomial x 2 – 2x + 3, find the polynomial whose roots are 1. 𝛼 + 2, 𝛽 + 2 2. (𝛼-1)/(𝛼+1), (𝛽-1)/(𝛽+1) Read More »

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. Read More »

Two water taps together can fill a tank in 9 3/8 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. Read More »

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. Read More »

If 𝛼, β are zeroes of quadratic polynomial 5x 2 + 5x + 1, find the value of 1. 𝛼2 + 𝛽2 2. 𝛼-1 + 𝛽-1 Read More »

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 the following types of graph represents p(t)? Read More »

Find the value of ‘p’ for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other. Read More »

Find the discriminant of the quadratic equation 4x^2 – 5 = 0 and hence comment on the nature of the equation. Read More »

Find the value of ‘p’ for which the quadratic equation px (x – 2) + 6 = 0 has two equal roots. Read More »

If one zero of the polynomial p(x) = 6x^2 + 37 x – (k-2) is reciprocal of the other, then find the value of k. Read More »