Question

1.
2.
The general form of quadratic equation is
If a quadratic equation ax2 + bx + c = 0 is satisfied by more than two distinct roots, then f(x) = 0
becomes as an
3.
If ax? + bx + c = 0 is a quadratic equation, then the discriminant is
4.
If a,ß are the roots of quadratic equation, then the quadratic equation is
The value of k for which the equation x2 + 2 (k+ 1) x + k2 = 0 has equal roots is
5.
6.
The roots of x2 - 6x + 8 = 0 are
7.
If o,ß are the roots of a quadratic equation then |a - B1 =​

Answer 1

Answer:

2. (m+n)α=a−b,mnα2=ac

⇒α=a(m+n)−b,mnα2=ac

⇒α2=a2(m+n)2b2,mnα2=ac

⇒mnα2=ac

⇒mna2(m+n)2b2=ac where α2=a2(m+n)2b2

⇒mn.a2(m+n)2

3. Discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is b2 − 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3 − 4a3c − 27c2.

4. Given x2−2(k+1)x+k2=0 has real and equal roots

As we know that 

for a quadratic equation to have real and equal roots ,discriminant should be zero

⟹(−2(k+1))2−4(1)(k2)=0

⟹(k+1)2−k2=0

⟹2k+1=0

⟹k=−21

6.. Explanation:

Solve:

x2−6x+8=0

Factor.

(x−2)(x−4)=0

Solve for x.

x−2=0

x=2

x−4=0

x=4

x=2,4

graph{y=x^2-6x+8 [-10, 10, -5, 5]}