Question

if alpha and betaa are zeroes of the polynomial of the quadratic polynomial x²-6x+a find the value of a if 3a+2B=30​

Answer 1

Your Question:

There's ambiguity in the question, So Question is repeated.

Correct Question:

If α and β are zeroes of the Quadratic polynomial x²-6x+a; find the value of 'a' if 3α+2β=20.

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Your Answer:

We know

${\\So, \:\:\alpha\beta=a\rightarrow\rightarrow\rightarrow\rightarrow(1)\\ \alpha+\beta=6\rightarrow\rightarrow\rightarrow\rightarrow(2)}$

We have

${3\alpha+2\beta=30}$

--------(3)

Now, Solving equation (2) and (3)

We will get

${\tt {\alpha=8 \:\:and\:\:\beta=-2}}$

${So,\alpha\beta=a=(8)(-2)=-16}$

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$\Huge{\red{\underline{\text{Additional}}}}$

The following question is from Polynomial

Some formulas of Polynomial Chapter

• α+β=−b/a
• αβ=c/a

This Question can also be solved by using Quadratic Equation

Answer 2

Question:

• if alpha and betaa are zeroes of the polynomial of the quadratic polynomial x²-6x+a find the value of a if 3a+2B=30.

SOLUTION:

Alpha and beta are roots of x^2-6x+a

So, alpha+beta = -(-6)/1 = 6

Multiplying it with 2, we get

2alpha + 2 beta = 12 ....(1)

Also, 3alpha + 2beta = 30....(2)

Solving, (1) and (2), we get

alpha = 18

So, beta = -12

So, alpha*beta = c/a

18*(-12) = a

a = -216.

So, the value of a will be -216.

Hope this helps