Question

if alpha,beta are roots of x2+3x-10=0 then alpha+beta=

Answer 1

Solution :-

First, let's find the zeroes of the polynomial x² + 3x - 10 = 0,

=> x² + 3x - 10 = 0

=> x² + (5 - 2)x - 10 = 0

=> x² + 5x - 2x - 10 = 0

=> x(x + 5) - 2(x + 5) = 0

=> (x - 2) (x + 5) = 0

.°. Either, (x - 2) = 0 or, (x + 5) = 0

=> x = 2 or, => x = -5

Hence, the zeroes of the polynomial are 2 and -5.

Now,

Let α = 2 & β = -5

According to question,

= α + β

= 2 + (-5)

= 2 - 5

= -3

Hence, the value of α + β is -3.

Answer 2

✯✯ QUESTION ✯✯

If alpha , beta are roots of x²+3x-10=0 then alpha + beta = ?

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✰✰ ANSWER ✰✰

$\implies\tt{{x}^{2}+3x-10=0}$

➥By Splitting Middle Term : -

$\implies\tt{{x}^{2}+(5x-2x)-10=0}$

$\implies\tt{{x}^{2}+5x5x-2x-10=0}$

$\implies\tt{x(x+5)-2(x+5)=0}$

$\implies\tt{(x-2)(x+5)}$

• x (α) = 2
• x (β) = -5

➮Now, we have to find the values of alpha(α) + beta(β) : -

➥Putting Values : -

$\implies\tt{\alpha+\beta}$

$\implies\tt{2+(-5)}$

$\implies\tt{2-5}$

$\implies\tt{-3}$

☛So , the value of alpha+beta is -3..