Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficient a) 5x^2-29x+20.​ pls answer fast

Answer 1

Step-by-step explanation:

this the answer for question

Answer 2

Answer:

x = 5 , 5

Note:

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

★ In order to find the zeros of the given polynomial , equate it to zero .

★ A quadratic polynomial can have atmost two zeros.

★ The general form of a quadratic polynomial is given by : ax² + bx + c .

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

• Sum of zeros , (A + B) = -b/a

• Product of zeros , (A•B) = c/a

Solution:

Here,

The given quadratic polynomial is ;

5x² - 29x + 20

Clearly,

a = 5

b = -29

c = 20

Now,

Let's find the zeros of the given quadratic polynomial by equating it to zero .

Thus,

=> 5x² - 29x + 20 = 0

=> 5x² - 25x - 4x + 20 = 0

=> 5x(x - 5) - 4(x - 5) = 0

=> (x - 5)(5x - 4)

=> x = 5 , 4/5

Now,

Sum of zeros = 5 + 4/5 = (25 + 4)/5 = 29/5

Also,

-b/a = -(-29)/5 = 29/5

Clearly,

Sum of zeros = -b/a

Now,

Product of zeros = 5 ×(4/5) = 4

Also,

c/a = 20/5 = 4

Clearly,

Product of zeros = c/a

Hence verified