Polynomials Tes...

If the sum of zeros of the polynomial 12ax² + (5 – b)x + 10 is 0 and the product of all zeros is 1, then the zeros of the polynomial are

If the sum of the product of the zeros taken two at a time of the polynomial f(x) = 12x³ + 2qx² – 5px + 18 is -15 and the sum of all zeros is 10, then the value of p + q is

If 8 and d are the roots of the quadratic equation 2x² – 10rx + 18 = 0, then the value of 'r' is

Find out the cubical polynomial with sum, sum of the product of its zeros taken two at a time, and product of its zeros as 11, -15 and -9, respectively.

If s and r are the zeros of the polynomial f(x) = 4x² – 8q(x + 1) + 8c, then is equal to

When 2x³ + 8x² – 4x -12 is divided by x² + 2x – 1, the quotient and the remainder respectively are:

What should be subtracted from f(x) = 9x³ – 12x² + 40x – 72 so that f(x) is exactly divisible by 3x² – 2x + 1?

If one zero of the polynomial f(x) = x² – (k² – 2)x + 8 is double of the other zero, then k is equal to

If f(x) = dx⁷ + px⁶ – gx⁵ + ax² – fx + s, then which of the following is true?

What is the number of zeroes of the polynomial y = p(x) in the given graph?

If a, b and c are roots of the equation 6x³+ 11x² – 5 = 0, then the equation whose roots are (9a – 2b – 3c), (2a -3b – 9c) and (-9a + 7b + 14c) is

For x³ + x² – 3x + 6 to be a factor of x⁵ + 2x⁴ + ax² – b + 2, the values of a and b should respectively be

If a and b are roots of the given equation, then which of the following equations has its roots as 2a and 2b?

f(x) = 10x²- 32x + 24 = 0

Which of the following should be subtracted from the dividend x⁸ - 6x + 8 so that -2 + x² as its factor?

If x³ + ax² + bx + 12 leaves remainder 4 when divided by (x - 1), which of the following is the value of a + b?

The area of a trapezoidal shaped wooden board is 36x⁴ + 6x³ - 69x² - 8x + 28. The lengths of the parallel sides of the shape are 15x² - 4x + 4 and 9x² + 8x - 18. What will be the height of the wooden board?

The perimeter of a square-shaped plot is 16x²+ 8x + 16. What will be the area of a square-shaped garden whose area isof the area of the given plot?

An automobile company manufactures 35x⁶ + 63x⁵ + 56x⁴ + 64x³ + 27x² + 24x + 21 cars. If there are 7x³ + 3 showrooms in a city, then how many cars are there in one showroom?

If the weights of two different quantities are (3x³ - 6x² - 4x + 8) kg and (5x³ - 10x² + 2x - 4) kg, then what is the biggest measure that can weigh both the quantities?

The radius and height of a cylindrical pipe are (5x² - 27x) m and (3x²- 20x) m, respectively. Find the surface area of the pipe which is open from both the sides when x = .

Find the roots of, if the polynomial 2x⁵+ 4x³– 3x²- px + q is exactly divisible by x²– 3.

Consider the following statements:

Statement-I: One of the factors of the polynomial 3x³– 12x²+ 4x – 16 is (2x + 4).
Statement-II: When 8x⁶+ 7x⁵– 4x⁴- x³+ 2x²+ 6 is divided by 2x³+ x²– 4, the coefficient of the highest degree variable in remainder is .

Which of the following options holds?

What will be the value of if m, n and o are the zeros of the polynomial px³ – qx² + 5x - 2?

Match the following:

Column I	Column II
(L) If p(x) = x2 - k and x = 7 is a zero of p(x), then the value of k is	(I)
(M) In the polynomial equation (-8p + 10)e2 - 11e - 6 = 0, if one of the roots is the negative reciprocal of the other, then the value of p is	(II) 35
(N) In the polynomial equation x3 + 3 + 13x + d = 0, if the product of the roots is -7, then the value of d is	(III) 49

Find the values of

(i) 1296A + 36C + D
(ii) -2592A + B - 72C - 2D
(iii) B

if 6 and -6 are the zeros of Ax⁵ + B + Cx³ + Dx.