Question

If alpha and beta are the zeros of 2 x square - 5 x + 3 find the value of Alpha square plus beta square second one upon alpha + one upon beta

Answer 1

Step-by-step explanation:

Given -

• α and β are zeroes of polynomial p(x) = 2x² - 5x + 3

To Find -

1. Value of α² + β²
2. Value of 1/α + 1/β

Now,

→ 2x² - 5x + 3

→ 2x² - 2x - 3x + 3

→ 2x(x - 1) - 3(x - 1)

→ (2x - 3)(x - 1)

Zeroes are -

→ 2x - 3 = 0 and x - 1 = 0

→ x = 3/2 and x = 1

Then,

The value of α² + β² is

→ (3/2)² + (1)²

→ 9/4 + 1

→ 9+4/4

→ 13/4

And

The value of 1/α + 1/β is

→ 1/1 + 1 ÷ 3/2

→ 1 + 2/3

→ 3+2/3

→ 5/3

Answer 2

$\bigstar$ Question : -

If α and β are the zeros of 2x²-5x+3 find the

value of 1) α²+ β² 1) upon  α+ one upon β

$\bigstar$ Solution :-

$\bigstar$ Given :-

• α and β are zeroes of polynomial p(x) = 2x² - 5x + 3

$\bigstar$ To Find :-

• Value of α² + β²

• Value of 1/α + 1/β

$\bigstar$ Explanation :-

$\star$ Comparing the given equation 2x²-5x+3 with ax²+bx+c , we get ,

⇒ a = 2 , b = -5 , c = 3

$\star$ Now , sum of roots , α+ β = -b/a

⇒ α+ β = -(-5)/2

⇒ α+ β = 5/2 ...(1)

$\star$ Product of roots , αβ = c/a

⇒ αβ = 3/2 ...(2)

$\bigstar$ Case-1 : To find the value of α² + β²

$\star$ Squaring eq. (1) on both sides , we get ,

⇒ (α+ β)² = (5/2)²

⇒ α²+ β²+2αβ = 25/4

⇒ α²+ β² = 25/4 - 2(3/2)   [from (2)]

⇒ α²+ β² = 25/4 - 6/2 = (25-12)4 = 13/4

⇒ α²+ β² = 13/4

$\bigstar$ Case - 2 :   To find the Value of 1/α + 1/β

$\implies \frac{1}{\alpha } +\frac{1}{\beta } \\\\\implies \frac{\alpha+\beta }{\alpha.\beta } \\\\\implies \frac{\frac{5}{2} }{\frac{3}{2} }\:[\:From (1)\:\&\:(2)\:]\\\\ \implies \frac{5}{3}$

                                                 

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