Question

if alpha and beta are zeros of polynomial 3xsquare-24x+143 then alpha+beta=​

Answer 1

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Answer 2

Answer:

Required value of $\alpha + \beta$is 8.

Step-by-step explanation:

Given polynmial is $3 {x}^{2} - 24x + 143$

Let f(x)$= 3 {x}^{2} - 24x + 143$

Given $\alpha$and $\beta$are two zeros of $f(x) = 0$

Now,$f(x) = 0$

$3 {x}^{2} - 24x + 143 = 0$

We know,

$x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a}$

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

Here,

$a = 3 \\ b = - 24 \\ c = 143$

So,$x = \frac{ - ( - 24)± \sqrt{ {( - 24)}^{2} - 4 \times 3 \times 143} }{2 \times 3}$

Therefore $x = \frac{24± \sqrt{ - 1140} }{6}$

So,$\alpha = \frac{24 + \sqrt{ - 1140} }{6}$and $\beta = \frac{24 - \sqrt{ - 1140} }{6}$

Now,$\alpha + \beta = \frac{24 + \sqrt{ - 1140} }{6} + \frac{24 - \sqrt{ - 1140} }{6} = \frac{24 + \sqrt{ - 1140} + 24 - \sqrt{ - 1140} }{6} = \frac{24 + 24}{6} = \frac{48}{6} = 8$