Question

if alpha and beta are are the zeros of the polynomial 2x square plus 7x plus 5 find the value of Alpha square plus beta square​

Answer 1

Answer:

29/5

Explanation:

Given polynomial,

⇒ 2x² + 7x + 5

On comapring with the general form of equation ax² + bx + c

• a = 2
• b = 7
• c = 5

Here, α and β are the zeros of the quadratic polynomial.

Then,

• α + β = -b/a = -7/2
• αβ = c/a = 5/2

Solving for :-

⇒ α² + β²

⇒ (α + β)² - 2αβ

Substituting the values,

⇒ (-7/2)² - 2(5/2)

⇒ 49/4 - 5

⇒ 49 - 20/5

⇒ 29/5

Required answer: 29/5

_____________________

Identity used :-

a² + b² = (a + b)² - 2ab

Answer 2

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$\alpha \: \: and \: \beta \: \: are \: the \: zeros \: of \: the \\ \: polinolial \: \: \: 2 {x}^{2} + 7x + 5 \\ so \\ \\ \alpha + \beta = - \frac{7}{2} \\ \\ \alpha \beta = \frac{5}{2} \\ now \\ \red \odot \:\: { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta) }^{2} - 2 \alpha \beta \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {( - \frac{7}{2} )}^{2} - 2 \times \frac{5}{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{49}{4} - 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{49 - 20}{4} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{29}{4}$