Math  /  Algebra

QuestionIf the proauct of xeroes of the polynomial ax218x6Δa x^{2}-18 x-6 \Delta is 4 . Find the the value of aa.

Studdy Solution

STEP 1

1. The polynomial given is ax218x6Δa x^2 - 18 x - 6 \Delta.
2. The product of the zeros of a quadratic polynomial ax2+bx+ca x^2 + b x + c is given by ca\frac{c}{a}.
3. We are given that the product of the zeros is 4.

STEP 2

1. Identify the coefficients aa and cc in the polynomial ax218x6Δa x^2 - 18 x - 6 \Delta.
2. Use the formula for the product of the zeros to set up an equation.
3. Solve the equation to find the value of aa.

STEP 3

Identify the coefficients aa and cc in the given polynomial ax218x6Δa x^2 - 18 x - 6 \Delta.
The coefficients are: a=a a = a b=18 b = -18 c=6Δ c = -6 \Delta

STEP 4

Use the formula for the product of the zeros of the quadratic polynomial ax2+bx+ca x^2 + b x + c, which is ca\frac{c}{a}.
For the given polynomial, the product of the zeros is: 6Δa \frac{-6 \Delta}{a}

STEP 5

Set up the equation using the given product of the zeros, which is 4:
6Δa=4 \frac{-6 \Delta}{a} = 4

STEP 6

Solve the equation for aa:
6Δ=4a -6 \Delta = 4a a=6Δ4 a = \frac{-6 \Delta}{4} a=3Δ2 a = -\frac{3 \Delta}{2}
Solution: The value of aa is 3Δ2-\frac{3\Delta}{2}.

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