Polynomials Tes...

If y - 2 and y - are the factors of py² + 5y + r, then

If , are roots of ax² + bx + b = 0, then
(a and b are of the same sign)

Which of the following is the value of the coefficient b in the polynomial y = ax² + bx + c in the given graph? (Given: a ≠ 0)

If a, b and c are the roots of the cubic equation x³ - 7x² + 14x - 8 = 0, then find the value of a² + b² + c².

The sum of zeros, the product of zeros, and the sum of the product of zeros taken two at a time of the polynomial x³ + bx² + cx + d are 3, -24 and -10, respectively. What are the respective values of b, c and d?

What is the product of sum of zeros and reciprocal of product of zeros of the polynomial 25x² + 79x + 12?

Find the value of g(x), if on dividing 3x² + 5x + 2 by g(x) the quotient and the remainder are and , respectively.

If kx + 1 is a factor of 2x³ - x² - 5x - 2, find the value of k.

What is the minimum degree of the polynomial for the plotted graph?

When the polynomial x³ + 3x² – 6ax – 5 is divided by (x – 1), the remainder is P; and when the polynomial x³ + ax² – 15x + 20 is divided by (x + 2), the remainder is Q. Find the value of 'a' if 2P + Q = 0.

If 2 and -2 are the zeros of the polynomial x⁴ - 5x² + 4, what are the other possible zeros of the polynomial?

Which of the following is/are the factor(s) of ?

If ab = q and a + b = p, then what are the factors of the algebraic expression x² + px + q?

If one of the zeros of the polynomial x³ + 2x² - 9x - 18 is -2, what are the other possible zeros?

If and are the roots of the equation x² - p(x + 1) - q = 0, then what is the value of ?

The area of a parallelogram is (x⁵ + 4x³ + 45x²+ 32x - 38) m and the height of the parallelogram is (x²+ x - 1) m. Find the base of the parallelogram.

A triangular park with length of the first side (3x³ + 7x² - 8) m and length of the second side (5x³ - 9x² - 2) m has perimeter (12x³ - 8x² - 10) m. Find the length of the third side of the park.

In the first week, Priya spent Rs. (10x³ + 5x² + 2) for buying pencils. In the second week, she bought (9x² + 10) pencils and the price of each pencil was Rs. (2x + 4). How much did she spend altogether in two weeks?

If the weight of one basket is (2x³ – 8x² + x – 4) kg and the weight of another basket is (4x³ + 12x² + 2x + 6)kg, then what will be the biggest measure that can measure both quantities exactly?

The radius and slant height of a cone are (6x² + 5x) m and (3x² + 4x + 1) m, respectively. Find the lateral surface area of the right cone when.

On dividing x³ + 2x² - 4x + 7 by x + 2, the quotient and the remainder are x² - a and 15, respectively. What is the value of a?

Which of the following options holds?

Statement I: The polynomial 14x³ - 35x² - 16x + 40 has (2x - 5) as one of its factors.
Statement II: When the polynomial 5x⁵ + 7x⁴ - 3x³ + 6x² - 10 is divided by (x² + 3x - 1), then the value of constant term in remainder is -90.

Let R₁ and R₂ be the remainders when the polynomials x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6 are divided by x + 1 and x - 2, respectively.

Which of the following is the value of a if 2R₁ + R₂ = 6?

Match the following columns

(P) If one of the zeros of the polynomial f(x) = x2 + 24x + 242 is 22 and the other zero is half of the first zero, then q is equal to	(i) -40
(Q) If the sum of the zeros of the polynomial f(x) = 8x3+ 5kx2+ 6x + 10 is 25, then k is equal to	(ii) -(1 + r)
(R) If the polynomial f(x) = qx4+ rx2– sx + p is exactly divisible by g(x) = x2+ sx – p, then q(p + s2)is equal to	(iii) 9

If 2 and -2 are zeros of the polynomial Qx⁵ – Px⁴ + Zx³ + Rx² + M, find the values of the following:

(i) 8R + 2M
(ii) 4Q + Z