Question 10
Pls tell the answer
Answers
Answer :
a = 1
Explanation :
Let f(x) = ax³ + 3x² - 3
Let p(x) = 2x³ - 5x + a
When f(x) / (x - 4)
Leaves same remainder.
To find remainder find the zero of x - 4
To find zero of x equate x - 4 to 0
x - 4 = 0
x = 4
So, f(4), p(4) are the remainders of f(x) and p(x) respectively
Since remainders are equal
So, f(4) = p(4)
a(4)³ + 3(4)² - 3 = 2(4)³ - 5(4) + a
a(64) + 3(16) - 3 = 2(64) - 20 + a
64a + 48 - 3 = 128 - 20 + a
64a + 45 = 108 + a
64a - a = 108 - 45
63a = 63
a = 63/63
a = 1
Extra info
Zero of a polynomial : We say that a zero of a polynomial p(x) is the value of x, which p(x) is equal to zero. This value is also called a root of the polynomial p(x).
Polynomial : An algebraic expression in which the variables involved have only non-zero negative integral powers is called a polynomial.
Cubic polynomial : A polynomial of degree 3 is called the cubic polynomial. A cubic polynomial can have 3 zeroes.
* If the variable in a polynomial is x, we made not the polynomial by p(x), q(x) or r(z) etc.
e.g. p(x) = 3x² + 2x + 1
q(x) = x³ - 5x² + x - 7
r(y) = y³ - 1
t(z) = z² + 5z + 3