Question

find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. x^2-5x​

Answer 1

Step-by-step explanation:

${x}^{2} - 5x = 0 \\ x(x - 5) = 0 \\ x = 0 \: or \: x = 5$

Verification:

From the quadratic equation, a=1, b=-5, c=0

Sum of roots is 0+5=5.

So, sum of roots is -b/a=-(-5)/1=5/1=5

Product of roots is 0x5=0.

So, product of roots is c/a=0/1=0.

Hence proved

Thank you

Answer 2

Answer:

x = 0 , 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 ;

x² - 5x

The given quadratic polynomial can be rewritten as ; x² - 5x + 0

Clearly,

a = 1

b = -5

c = 0

Now,

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

Thus,

=> x² - 5x = 0

=> x(x - 5) = 0

=> x = 0 , 5

Now,

Sum of zeros = 0 + 5 = 5

Also,

-b/a = -(-5)/1 = 5

Clearly,

Sum of zeros = -b/a

Now,

Product of zeros = 0×5

Also,

c/a = 0/1 = 0

Clearly,

Product of zeros = c/a

Hence verified