Question

From the given quadratic equation 3 X square + 7 x + 4 is equal to zero find the value of Alpha square plus beta square

Answer 1

Answer: the answer is -8/3

Step-by-step explanation:

The method is explained in the image below

Answer 2

From the given quadratic equation 3 X square + 7 x + 4 is equal to zero the value of Alpha square plus beta square is 25/9

• The roots of the given quadratic equation $3x^{2} +7x+4=0$ are alpha and beta.
• Now from vieta's methods we can determine the relation between coefficients and roots of the quadratic equation.  
• From this we can get alpha + beta = $-\frac{7}{3}$ and alpha*beta = $\frac{4}{3}$
• Now alpha^2+beta^2 = (alpha+beta)^2- 2*alpha*beta
• So alpha^2+beta^2= $(-\frac{7}{3} )^{2} -2*\frac{4}{3}$ = $\frac{25}{9}$
• So the required value is 25/9