Apply division algorithm to find the quotient q(x) and remainder r(x) when f(x) = x³ − 6x² + 11x − 6 is divided by g(x) = x² + x + 1 Video Explanation Watch the video explanation below: Solution Given: f(x) = x³ − 6x² + 11x − 6 g(x) = x² + x + […]
If the zeroes of the polynomial f(x) = x³ − 12x² + 39x + k are in A.P., find the value of k Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = x³ − 12x² + 39x + k Let the zeroes of the polynomial be in A.P. ∴ Let the zeroes
If the zeroes of the polynomial f(x) = ax³ + 3bx² + 3cx + d are in A.P., prove that 2b³ − 3abc + a²d = 0 Video Explanation Watch the video explanation below: Proof Given polynomial: f(x) = ax³ + 3bx² + 3cx + d Let the zeroes of the polynomial be in A.P.
Find the condition that the zeroes of the polynomial f(x) = x³ + 3px² + 3qx + r may be in A.P. Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = x³ + 3px² + 3qx + r Let the zeroes of the polynomial be in A.P. ∴ Let the zeroes be:
If the zeroes of the polynomial f(x) = 2x³ − 15x² + 37x − 30 are in A.P., find them Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = 2x³ − 15x² + 37x − 30 Let the zeroes of the polynomial be in A.P. ∴ Let the zeroes be: a −
If the Zeroes of the Polynomial f(x) = 2x³ − 15x² + 37x − 30 Are in A.P., Find Them Read More »
If 4 is a zero of the cubic polynomial x³ − 3x² − 10x + 24, find its other two zeroes Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = x³ − 3x² − 10x + 24 Given that x = 4 is a zero of the polynomial. Step 1: Verify x
If 4 Is a Zero of the Cubic Polynomial x³ − 3x² − 10x + 24, Find Its Other Two Zeroes Read More »
Find all zeroes of the polynomial 3x³ + 10x² − 9x − 4, if one of its zeroes is 1 Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = 3x³ + 10x² − 9x − 4 Given that x = 1 is a zero of the polynomial. Step 1: Verify x =
Find All Zeroes of the Polynomial 3x³ + 10x² − 9x − 4, If One of Its Zeroes Is 1 Read More »
Find the cubic polynomial whose sum of zeros is 3, sum of the product of its zeros taken two at a time is −1 and product of its zeros is −3 Video Explanation Watch the video explanation below: Solution Given: Sum of zeros = 3 Sum of products of zeros taken two at a time
Verify that 2, 1 and 1 are the zeros of the cubic polynomial g(x) = x³ − 4x² + 5x − 2 and verify the relationship between zeros and coefficients Video Explanation Watch the video explanation below: Solution Given polynomial: g(x) = x³ − 4x² + 5x − 2 Step 1: Verify the Given Zeros
Verify that 1/2, 1 and −2 are the zeros of the cubic polynomial f(x) = 2x³ + x² − 5x + 2 and verify the relationship between zeros and coefficients Video Explanation Watch the video explanation below: Solution Given polynomial: f(x) = 2x³ + x² − 5x + 2 Step 1: Verify the Given Zeros