Question

11)a and b are the roots of quadratic equation x²-ax +b =0 then *

1 point

a=0,b=1

a=-2,b=1

a=1,b=-2

None of these

12)Roots of quadratic equation x²+25=0 are *

1 point

5,5

-5,-5

+5,-5

None of these

13)If sum and product of zero's of a quadratic polynomial are 3 and -2 then polynomial is : *

1 point

X²-3x+2

X²-3x-2

X²+3x+2

X²-2x+3

​

Answer 1

Answer:

1. The value of a and b are either a=0,b=0 or a=1, b=-2.
2. +5,-5
3. x^2+3x+2

Step-by-step explanation:

1. If a quadratic equation is defined as ax^2+bx+c=0

ax^2+bx+c=0 and α and β are roots, then

\alpha +\beta=\frac{-b}{a}α+β=

a÷

−b

....(1)

\alpha \times \beta=\frac{c}{a}α×β=

a÷

c

.... (2)

The given equation is

x^2+ax+b=0x

2

+ax+b=0

The a and b are roots of quadratic equation. Using equation (1) we get

a+b=\frac{-a}{1}a+b=

1

−a

a+b=-aa+b=−a

2a+b=02a+b=0 ... (3)

Using equation (2), we get

a\times b=\frac{b}{1}a×b=

1

b

ab-b=0ab−b=0

b(a-1)=0b(a−1)=0

Equate each factor equal to 0.

b=0b=0

a=1a=1

If b=0, then by equation (3) a=0.

If a=1, then by equation (3) b=-2.

Therefore the value of a and b are either a=0,b=0 or a=1, b=-2.

2. Considering the equation,

• x^2–25=0

x^2=25

x=√25

x=+5,-5

3. Let the quadratic polynomial ax^2+bx+c and its zeros be alpha and beta.

We have,

◾Alpha + Beta = -3 = -b/a

-b/a = -3/1

◾Alpha x Beta = 2= c/a

c/a= 2/1

a=1, b=3,c=2

The polynomial will be x^2+3x+2

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