Short Answer Type
Q1: Find remainder when x^{3} − αx^{2} + 6 − α is divided by (x  a).
Q2: If the zeroes of the quadratic polynomial x^{2} + (α + 1 ) x + b are 2 and 3, then find the value of a and b.
Q.3. If a and b are zeroes of the polynomial f (x) = 2x^{2} − 7x + 3, find the value of α^{2} + b^{2}.
Q.4. Find the zeroes of the quadratic polynomial x^{2} + x − 12 and verify the relationship between the zeroes and the coefficients.
Q5: If p and q are zeroes of f (x) = x^{2} − 5x + k, such that p − q = 1 , find the value of k.
Q6: Given that two of the zeroes of the cubic polynomial αx^{3} + bx^{2} + cx + d are 0, then find the third zero.
Q.7. If one of the zeroes of the cubic polynomial x^{3} + αx^{2} + bx + c is 1, then find the product of the other two zeroes.
Q8: If ab, a a+b , are zeroes of x^{3} − 6x^{2} + 8x , then find the value of b
Q9: Quadratic polynomial 4x^{2} + 12x + 9 has zeroes as p and q . Now form a quadratic polynomial whose zeroes are p − 1 and q − 1
Long Answer Type
Q10: p and q are zeroes of the quadratic polynomial x^{2} − (k + 6 ) x + 2(2 k − 1) . Find the value of k if 2(p + q) = p q
Q11: Given that the zeroes of the cubic polynomial x^{3} − 6 x^{2} + 3 x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
Q12: If one zero of the polynomial 2x^{2}−5x−(2k + 1) is twice the other, find both the zeroes of the polynomial and the value of k.
Q.13: Using division show that 3y^{2} + 5 is a factor of 6y^{5} + 15y^{4} + 16y^{3} + 4y^{2} + 10y − 35 .
Q14: If (x  2) and [x  1/2 ] are the factors of the polynomials qx^{2} + 5x + r prove that q = r.
Q15: Find k so that the polynomial x^{2} + 2x + k is a factor of polynomial 2x^{4} + x^{3}  14x^{2} + 5x + 6. Also, find all the zeroes of the two polynomials.
126 videos477 docs105 tests

1. What is a polynomial? 
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5. How do I add or subtract polynomials? 

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