Question

Question 10 answer please

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :}}}}$

$a = 1$

$\mathfrak{\large{\underline{\underline{Explanation :}}}}$

Let f(x) = ax³ + 3x² - 3

Let p(x) = 2x³ - 5x + a

$f(x)\div(x-4)\\and\:p(x)\div(x-4)$

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

$\tt{\boxed{a = 1}}$

$\mathfrak{\large{\underline{\underline{Additional\:info :}}}}$

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