Question

if one zero of f (x) = 4x2 + px - 25 is the negative of the other zero , what is the value of p ?

Answer 1

Answer :

p = 0

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

★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² - (α + ß)x + αß ] , k ≠ 0.

★ The discriminant , D of the quadratic polynomial ax² + bx + c is given by ;

D = b² - 4ac

★ If D = 0 , then the zeros are real and equal .

★ If D > 0 , then the zeros are real and distinct .

★ If D < 0 , then the zeros are unreal (imaginary) .

Solution :

Here ,

The given quadratic polynomial is ;

f(x) = 4x² + px - 25 .

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

a = 4

b = p

c = -25

Now ,

According to the questions , one of the zero of the given polynomial f(x) is the negative of the other .

Thus ,

Let t and -t be the zeros of the given quadratic polynomial f(x) .

Now ,

=> Sum of zeros = -b/a

=> t + (-t) = -p/4

=> 0 = -p/4

=> p = 0 × -4

=> p = 0

Hence , p = 0 .

Answer 2

Given ,

• The polynomial is F(x) = 4(x)² - px - 25

• The one zeroes of given polynomial is negative of the other zeroes

Let , one zeroes be " S "

Then , other zeroes = " -S "

We know that , the sum of zeroes is given by

$\boxed{ \sf \alpha + \beta = - \frac{b}{a} }$

Thus ,

S + (-S) = -P/4

0 = -P/4

P = 0

Therefore ,

• The value of P is 0