Question

If alpha and beta are the roots of the equation x^2-3x+k=0 such that alpha=2alpha betah

Answer 1

Given α=2β and x2−3x+k=0

Sum of the roots=2β+β=−(−3/1)
⟹3β=3
=>β=1

Product of the roots=
k/1=2β×β
2β^2=k/1
Butβ=1
∴2=k1
⟹k=2

For more answers follow me

Answer 2

The value of k is 2.

Correct question:

Given:

• A quadratic equation ${x}^{2} - 3x + k = 0$
• If $\alpha$ and $\beta$ are roots, such that $\alpha = 2 \beta$

To find:

• Find the value of k.

Solution:

We know that,

If $\alpha$ and $\beta$ are roots of quadratic equation $\bf a {x}^{2} + bx + c = 0$

then

$\alpha + \beta = - \frac{b}{a}...eq1$

and

$\alpha \beta = \frac{c}{a}...eq2$

Step 1:

Find the value of $\beta$.

As, it is given that

$\alpha = 2 \beta$

place the value in eq1

$2 \beta + \beta = - \frac{ - 3}{1}$

$3 \beta = 3$

$\beta = 1$

Step 2:

Find the value of $\alpha$.

Put the value in given relationship

$\alpha = 2 \times 1$

$\alpha = 2$

Step 3:

Find the value of k.

Use equation 2.

$(2)(1) = \frac{k}{1}$

$\bf \red{k = 2 }$

Thus,

Value of k is 2.

Learn more:

1) If alpha and beta are the roots of the equation 2x^2 +3x +2 =0 ,find the equation whose roots are alpha +1 and beta +1

https://brainly.in/question/17062588

2) 3s²-6s+4 find the value of alpha / beta + beta / alpha +2 ( 1/alpha + 1/ beta)+ 3alpha beta

https://brainly.in/question/2749822

#SPJ3