Previous Year Mathematics Questions of Class 10 Chapter {Polynomials} for Examination 2023
One mark Questions
1. If α and β are the zeroes of the quadratic polynomial 2x2 – 13x + 6, then α + β= ……………… (CBSE 2020)
2. The maximum number of zeroes a cubic polynomial can have is …………… (CBSE 2020)
3. The Zeroes of the polynomial x2 – 3x – m(m + 3) are ………………. (CBSE 2020)
4. If one zero of the quadratic polynomial x2 – 5x – 6 is 6 then find the other zero.
5. Find the zeroes of polynomial √3 x2 – 8x + 4√3
6. If the graph of a polynomial intersects x – axis at exactly two points is it necessarily a quadratic polynomials.
7. Find the quadratic polynomial whose zeroes are -3 and -5.
Two mark Questions
1. A teacher asked 10 of his students to write a polynomial in one variable on a paper and then to handover the paper. The following were answers given by the students: 2x + 3, 3x2 + 7x + 2 , 4x3 + 3x2 + 2 , 5x3 – 7x + 2, 2x2 + 3 , 5x – ½ , ax3 + bx2 + cx + d ,
Answer the following questions:
(i) How many of the above ten, are not polynomials? (CBSE 2020)
(ii) How many of the above ten, are quadratic polynomials?
2. Divide (2x2 – x + 3) by (2 – x) and write the quotient and the remainder. (CBSE 2020)
3. If α and β are the zeroes of the quadratic polynomial f(x) = 5x2 - 7x + 1, find the value of α/β + α/β . (CBSE 2020)
4. If one of the zeroes of the quadratic polynomial p(x) = 4x2 – 8kx – 9 is equal in magnitude but opposite in sign. Of the other, find the value of K.
5. If one root of polynomial p(x) = 5x2 + 13x + m is reciprocal of other, then find the value of m.
6. For what value of h is the polynomial f(x) = 2x3 – hx2 + 5x + 9, exactly divisibility by (x + 2).
Three mark Questions
1. Find the quadratic polynomial, the sum of product of whose zeroes are -3 and 2 respectively. Hence find the zeroes. (CBSE 2020)
2. For what value of k is the polynomial f(x) = 3x4 – 9x3 + x2 + 15x + k completely divisible by 3x2 – 5? (CBSE 2019)
3. Find the zeroes of the quadratic polynomial 7y2 – 11/3 y – 2/3 and verify th relationship between the zeroes and the coefficients. (CBSE 2019)
4. What must be added to the polynomial P(x) = x4 + 2x3 – 2x2 + x – 1 so that the resulting polynomial is exactly divisible by x2 + 2x – 3 ?
5. If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x + 1, the remainder comes out to be ax + b, find a and b.
Four mark Questions
1. Find the zeroes of the polynomial f(x) = x3 – 5x2 – 2x + 24 if it is given that the product of its two zeroes is 12.
2. If x2 + x – 12 divides p(x) = x3 + ax2 + bx – 84 exactly, find a and b.
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