Question

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. If alphaand beta are the zeroep of the quadratic polynomial p(x)=5x^2-7x+1
find the value of 1/alpha+ 1/beta​

Answer 1

Step-by-step explanation:

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Answer 2

Answer :

1/α + 1/ß = 7

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

Solution :

Here ,

The given quadratic polynomial is ;

p(x) = 5x² - 7x + 1

Now ,

Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c , we have ;

a = 5

b = -7

c = 1

Also ,

It is given that , α and ß are the zeros of the given quadratic polynomial p(x) .

Thus ,

=> Sum of zeros = -b/a

=> α + ß = -(-7)/5

=> α + ß = 7/5

Also ,

=> Product of zeros = c/a

=> αß = 1/5

Now ,

=> 1/α + 1/ß = (ß + α)/αß

=> 1/α + 1/ß = (α + ß)/αß

=> 1/α + 1/ß = (7/5) / (1/5)

=> 1/α + 1/ß = (7/5) × (5

=> 1/α + 1/ß = 7

Hence , 1/α + 1/ß = 7 .