Question

If x is 2/3 and x is -3 are the roots of the quadratic equation ax²+bx+c find a and b

Answer 1

Step-by-step explanation:

Given -

• Zeroes are 2/3 and -3 of the quadratic equation ax² + bx + c

To Find -

• Value of a and b

As we know that :-

• α + β = -b/a

→ -3 + 2/3 = -b/a

→ -9 + 2/3 = -b/a

→ -7/3 = -b/a ......... (i)

And

• αβ = c/a

→ -3 × 2/3 = c/a

→ -6/3 = c/a ........ (ii)

Now, From (i) and (ii), we get :

a = 3

b = 7

c = -6

Verification :-

→ 3x² + 7x - 6

→ 3x² + 9x - 2x - 6

→ 3x(x + 3) -2(x + 3)

→ (3x - 2)(x + 3)

Zeroes are -

→ 3x - 2 = 0 and x + 3 = 0

→ x = 2/3 and x = -3

Hence,

The value of zeroes come same as zeroes given in the question it shows that our answer is absolutely correct.

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\implies$ x = -3

$\implies$ x = 2/3

$\large\underline\mathrm{Given:-}$

• zeroes are 2/3 and -3 of the quadratic equations ax²+bx+c

$\large\underline\mathrm{To \: find}$

• value of a and b

$\large\underline\mathrm{Solution}$

$\implies$ α + β = -b/a

$\implies$ -3 + 2/3 = -b/a

$\implies$ -9 + 2/3 = -b/a

$\implies$ -7/3 = -b/a. ...(1)

$\large\underline\mathrm{and,}$

$\implies$ αβ = c/a

$\implies$ -3 × 2/3 = c/a

$\implies$ -6/3 = c/a. ...(2)

$\implies$ a = 3

$\implies$ b = 7

$\implies$ c = -6

$\implies$ 3x² + 7x - 6

$\implies$ 3x² +9x - 2x - 6

$\implies$ 3x(x + 3) - 2(x + 3)

$\implies$ (3x - 2)(x + 3)

$\large\underline\mathrm{The \: value \: of \: x \: we \: get,}$

$\implies$ 3x - 2 = 0

$\implies$ 3x = 2

$\implies$ x = 2/3

$\implies$ x + 3 = 0

$\implies$ x = -3

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$