1) Verify the 1/2 ,1, -2 are zeroes of cubic polynomial 2x3
+ x2 -5 + 2. Also verify the relationship between the zeroes and their coefficients.
2) p and q are zeroes of the quadratic polynomial x2
– (k + 6)x + 2(2k – 1). Find the value of k if 2(p+q) =pq
3) m, n are zeroes of ax2
– 5x + c. Find the value of a and c if m + n = m. n = 10.
4) If a and b are zeroes of the x2
+ 7x + 7, find the value of a-1
5) Find remainder when x3
+ 6 – a is divided by (x – a).
6) If p and q are zeroes of f(x) = x2
– 5x + k, such that p -q = 1, find the value of k.
7) Given that two of the zeroes of the cubic polynomial ax3
+ cx + d are 0, then find the third zero.
8) If the zeroes of the quadratic polynomial x2
+ (a + 1) x + b are 2 and -3, then find the value of a and b.
9) If one of the zeroes of the cubic polynomial x3
+ bx + c is -1, then find the product of the other two zeroes.
10) If a-b, a a+b , are zeroes of x3
+ 8x, then find the value of b
11) Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2 respectively. Also, find its zeroes.
12) Given that the zeroes of the cubic polynomial x3
+ 3x + 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.
13) Check whether f(x) is a factor of g(x) by dividing f(x) by g(x):
f(x) = 2x4
– 2x + 2, g(x) = x2
+ 2x – 2.
14) Find the zeroes of the quadratic polynomial x2
+ x -12 and verify the relationship between the zeroes and the coefficients.
15) If a and b are zeroes of the polynomial f(x) = 2x2
– 7x + 3, find the value of a2
16) Quadratic polynomial 4x2
+ 12x + 9 has zeroes as p and q . Now form a quadratic polynomial whose zeroes are p -1 and q-1
17) If one zero of the polynomial 2x2
– 5x – (2k + 1) is twice the other, find both the zeroes of the polynomial and the value of k.
18) If m and n are the zeroes of the quadratic polynomial f(x) = x2 – px + q, then find the values of:
19) If the zeroes of the polynomial f(x) = x3
+ 39x + k are in A. P., find the value of k.
20) Using division show that 3y2
+ 5 is a factor of 6y5
+ 10y – 35.
3) 1/2 , 5
16) 4x2 + 20x + 25
18) -2q , p/q
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