CBSE Class 10 Answered
We have
f(x) = x3 - 6x2 + 11x - 6 and g(x) = x2 + x + 1
Clearly, degree of f(x) = 3 and degree of g(x) = 2.
Therefore, the degree of quotient is q(x) = 3 - 2 = 1 and the degree of remainder is r(x) less than 2.
Let quotient q(x) = ax + b and remainder r(x) = cx +d.
Using division algorithm, we have
f(x) = g(x) × q(x) + r(x)
Comparing the coefficient of same powers of x on both sides, we get
a = 1 [Comparing the coefficient of x3]
a + b = -6 [Comparing the coefficient of x2]
a + b + c = 11 [Comparing the coefficient of x]
b + d = -6 [Comparing the constant terms ]
Solving the above equations, we get the following values:
a = 1, b = -7, c = 17, and d = 1
∴ Quotient is q (x) = x - 7 and remainder is r(x) = 17x + 1
(i) We have:
f(x) = x3 - 6x2 + 11x - 6 and g(x) = x + 1
Clearly, degree of f(x) = 3 and degree of g(x) = 1. Therefore, the degree of quotient is q(x) = 3 - 1 = 2 and the degree of remainder is r(x) = 0
Let quotient q(x) = ax2 + bx + c and remainder r(x) = k.
Using division algorithm, we have
f(x) = g(x) × q(x) + r(x)
Comparing the coefficient of same powers of x on both sides, we get
a = 1 [Comparing the coefficient of x3]
a + b = -6 [Comparing the coefficient of x2]
b + c = -11 [Comparing the coefficient of x]
c + k = -6 [Comparing the constant terms ]
Solving the above equations, we get the following values:
a = 1, b = -7, c = 18, and k = -24
∴ Quotient is q (x) = x2 - 7x + 18 and remainder is r(x) = -24.
(i) We have:
f(x) = x3 - 6x2 + 11x - 6 and g(x) = x + 1
Clearly, degree of f(x) = 3 and degree of g(x) = 1. Therefore, the degree of quotient is q(x) = 3 - 1 = 2 and the degree of remainder is r(x) = 0
Let quotient q(x) = ax2 + bx + c and remainder r(x) = k.
Using division algorithm, we have
f(x) = g(x) × q(x) + r(x)
Comparing the coefficient of same powers of x on both sides, we get
a = 1 [Comparing the coefficient of x3]
a + b = -6 [Comparing the coefficient of x2]
b + c = -11 [Comparing the coefficient of x]
c + k = -6 [Comparing the constant terms ]
Solving the above equations, we get the following values:
a = 1, b = -7, c = 18, and k = -24
∴ Quotient is q (x) = x2 - 7x + 18 and remainder is r(x) = -24.