Determine the value of x in the diagram.

If x=2/3 and x=-3 are the roots of the equation ax^2+7x+b=0 find the values of a and b

Gnesinka [82]

ANSWER:

If x = $\frac{2}{3}$ and x = -3 are the roots of the equation, then values of a and b are 3, -6

SOLUTION:

Given, quadratic equation is $a x^{2}+7 x+b=0$ and its roots are -3 , $\frac{2}{3}$

We know that, for any quadratic equation of form $a x^{2}+b x+c=0$ with roots $x_{1} and x_{2}$ then,

Sum of roots $(x_{1} +x_{2})$ = $\frac{-b}{a}$

Product of roots ( $x_{1} \times x_{2})$ = $\frac{c}{a}$

Now, for given quadratic equation $x_{1}$ = -3 and $x_{2}$ = $\frac{2}{3}$

hence Sum of roots = $\frac{-7}{a}$

$x_{1} + x_{2} = \frac{-7}{a}$

$-3 + \frac{2}{3} = \frac{-7}{a}$

on solving we get "a" = 3

Now product of roots = $x_{1} \times x_{2} = \frac{b}{3}$

$-3 \times \frac{2}{3} = \frac{b}{3}$

b = -6

hence, the values of a and b are 3, -6.

7 0

3 years ago

A mother seal is fed 5 fish for every 2 fish for its baby. If mother is fed 8 fish how many does the baby get

iogann1982 [59]

5/2 = 8/x

5x = 16

x = 16/5

x = 3.2 or 3 1/5 fish

7 0

2 years ago

241 ten in base five?

igor_vitrenko [27]

241/5=48r1
48/5=9r3
9/5=1r4
1/5=0r4
=4431

7 0

3 years ago

Write the standard form of the equation of the circle described below.

Ahat [919]

Ce clasă ești sa văd daca te pot ajuta

7 0

2 years ago

Check image giving brainliest to first correct answer

Snowcat [4.5K]

Answer:

7

Step-by-step explanation:

So:a=3

b=(-2)

c=2

Substitute the numbers into each letters

so a is represented by 3,c by 2 and b -2

therefore giving us: 2

3+(-2)=9+(-2)=7

7 0

2 years ago