MATHS

posted by .

two zeros of cubic polynomial ax^3+3x^2-bx-6 are -1 and -2. find the third zero and values of a and b

• MATHS -

if x=-1, then -a + 3 + b - 6 = 0
a - b = -3
if x=-2, then -8a + 12 + 2b - 6 = 0
8a - 2b = 6
4a - b = 3
subtract them:
3a = 6
a = 2
in a-b=-3
2-b = -3
b = 5

so expression is
2x^3 + 3x^2 - 5x - 6

which is (x+1)(x+2)( ?x + ?)
by common sense, the last bracket must be
(2x -3)

so the third root is x=3/2

check:
(x+1)(x+2)(2x-3)
= (x^2 + 3x + 2)(2x-3)
= 2x^3 - 3x^2 + 6x^2 - 9x + 4x - 6
= 2x^3 + 3x^2 - 5x - 6 , all is good

Similar Questions

1. Algebra

Can someone please explain how to do these problems. 1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i. 2)list all of the possible rational zeros of f(x)= 3x^3-2x^2+7x+6. 3)Find all …
2. Math

Q.1)If one zero of the polynomial 3x2-kx-2 is 2 find the other zero.allso find the value of k. Q.2)If sum of the zeroes of the polynomial x2-x-k(2x-1) is 0,find the value of k Q.3)If 2 and 3 are the zeroes of the polynomial 3x2-2kx+2m …
3. Pre Calculus

1. Find all rational zeros of the polynomial. Then determine any irrational zeros, and factor the polynomial completely. 3x^4-11x^3+5x^2+3x 2. Find the polynomial with leading coefficient 1 that has a degree of 4, a zero of multiplicity …

Find all zeros of the following polynomial. Write the polynomial in factored form. f(x)=x^3-3x^2+16x-48 I put: x^2(x-3)+16(x=3) (x-3)(x^2+16) For zeros: x-3=0 x=0 **My teacher stated check the equation solution again. What is the value …
5. maths

Given that^2 is a zero of the cubic polynomial 6x3+2x2-10x-4^2, find its other two zeroes
6. maths

Given that root 2 is a zero of the cubic polynomial 6x3+2x2-10x-4root2, find its other two zeroes
7. algebra

Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function g(x)=5x©ù-28©ø-48x©÷-8x+7 if more than one zero, separate with …
8. algebra

Using the rational zeros theorem to find all zeros of a polynomial The function below has at least one rational zero. Use this fact to find all zeros of the function h(x)=7x^4-9x^3-41x^2+13x+6 if more than one zero, separate with commas. …
9. maths

If the zero of the polynomial x2 + px + q and double of the zero of 2x2 - 5x-3 respectively find values of p and q?
10. maths

If the zero of the polynomial x2 + px +q and double of the zero of 2x2 - 5x-3 respectively find values of p and q?

More Similar Questions