Question

Choose the quadratic equation having roots 2/3 and -1/2.​

Answer 1

Answer:

6x²- x -2

Step-by-step explanation:

roots :

• $\frac{2}{3}$ ( α )
• $\frac{-1}{2}$ ( β )

product of zeroes → αβ = $\frac{c}{a}$

∴ $\frac{2}{3}$ x $\frac{-1}{2}$ = $\frac{c}{a}$

$\frac{-2}{6}$ = $\frac{c}{a}$

∴ c = -2 , a = 6

sum of zeroes → α+β  = $\frac{-b}{a}$

$\frac{2}{3}$ + $\frac{-1}{2}$ = $\frac{-b}{a}$

$\frac{4}{6}$ + $\frac{-3}{6}$ = $\frac{-b}{a}$

$\frac{4-3}{6}$ = $\frac{-b}{a}$

$\frac{1}{6}$ = $\frac{-b}{a}$

∴ -b = 1

so b = -1

a = 6

∴substituting the values in the quadratic equation, ax²+bx+c

we get → 6x²- 1x -2

6x²- x -2

hope it helped! please mark as brainliest