Question

If $\alpha and \: \beta are the \: zeros \: of \: {4x}^{2} + 3x \: + 7 \: find \: \frac{1}{ \alpha } \: + \frac{1}{ \beta }$
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Answer 1

α and β are the zeroes of the polynomial 4x² + 3x + 7 .

• a = 4

• b = 3

• c = 7

★ Sum of the zeroes :

α + β = -b/a

⇒ α + β = -3/4

★ Product of the zeroes :

αβ = c/a

⇒ αβ = 7/4

Now,

1/α + 1/β [ Given ]

⇒ β + α / αβ

⇒ ( α + β ) / αβ

Substituting the values, we get

⇒ -3/4 / 7/4

⇒ -3/4 × 4/7

⇒ -3/7

The value of 1/α + 1/β is -3/7 .

Answer 2

Answer:

-3/7

Step-by-step explanation:

Answer is in the attachment