Question

7. If the roots of the quadratic equation x2 + 6x + k = 0 are equal, then the value of 'K' is
a) 9
b)-9
c) 8
d) 5​

Answer 1

Given that the roots of the quadratic equation x² + 6x + k are equal.

=> D = 0 (as when we have two equal roots, the Discriminant becomes equal to zero)

=> b² = 4ac (as D = b² - 4ac)

=> 6² = 4k

=> k = 36/4 = 9 (answer).

So, k = a) 9.

(As simple as that. ^^)

More:-

The standard form of any quadratic equation is ax² + bx + c = 0, where a ≠ 0 and a, b, c ∈ R.

How can we determine the symbols of a, b, and c?

• when the graph is curved upwards, the a has a postive value and vice versa.
• when the vertex is at 1st and 2nd quadrant, b has a negative value and for 3rd and 4th, it has a postive value.
• the value of c will depend on where the graph has intersected in Y - axis. For Y, it has postive and for Y′, it has negative.

A graph of a quadratic polynomial is a parabola.

Answer 2

Given :- . If the roots of the quadratic equation x² + 6x + k = 0 are equal, then the value of 'K' is

a) 9

b)-9

c) 8

d) 5

Solution :-

we know that, If A•x^2 + B•x + C = 0 ,is any quadratic equation, then its discriminant is given by;

• D = B^2 - 4•A•C
• If D = 0 , then the given quadratic equation has real and equal roots.

so, comparing x² + 6x + k = 0 with A•x^2 + B•x + C = 0 we get,

• A = 1
• B = 6
• C = k .

then,

→ D = 0

→ B² - 4ac = 0

→ 6² - 4 * 1 * k = 0

→ 4k = 36

→ k = 9 (a) (Ans.)

Hence, if roots are equal k is equal to 9 .

Learn more :-

JEE mains Question :-

https://brainly.in/question/22246812

. Find all the zeroes of the polynomial x4

– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

https://brainly.in/question/39026698