Question

If α, β are roots of x²
– 3ax + a²= 0, find the value(s) of a if α² + β² =
7/
4​

Answer 1

${\star{\red{\boxed{\bold{\boxed{Answer}}}}}}{\star}$

${\pink{1/4\: or\: -1/4}}$

⭐${\blue{Explanation}}$⭐

Find the value of $\alpha$+$\beta$ and $\alpha$$\beta$ from the polynomial

$\alpha$+$\beta$= -coefficient of x/ cofficient of x² = -(-3a)/1=3a

$\alpha$$\beta$=constant term / coefficient of x²=a²/1=a²

${\alpha}^{2}$+${\beta}^{2}$ = 7/4

($\alpha$+$\beta$)²-2$\alpha$$\beta$=7/4

Putting values of $\alpha$+$\beta$ and $\alpha$$\beta$

(3a)²-2a²=7/4

9a²-2a²=7/4

7a²=7/4

a²=1/4 → a = 1/4 or -1/4

$<marquee>HOPE IT HELPS✌✌</marquee>$

Answer 2

Answer:

$a = + \: or \: - \frac{ \sqrt{ 7} }{2}$

Step-by-step explanation:

${x}^{2} - 3ax + {a }^{2} \\ \alpha + \beta = \frac{ - ( - 3a)}{1} = 3a \\ \alpha \beta = {a }^{2}$

Now,

${ \alpha }^{2} + { \beta }^{2} = \frac{7}{4} \\ \\ = {( \alpha + \beta )}^{2} - 2( \alpha + \beta ) = \frac{7}{4} \\ \\ 3 {a}^{2} - 2 {a}^{2} = \frac{7}{4} \\ \\ {a}^{2} = \frac{7}{4} \\ \\ a = + \: or \: - \frac{ \sqrt{7} }{2}$

I hope this will help you...