Question

solve this question pllz......​

Answer 1

Answer:

x=-5

p(x)=2x^2+px+15=0

p(-5)=2(-5)^2+p(-5)+15=0

2x25-5p+15=0

50-5p+15=0

65-5p=0

-5p=-65

5p=65

p=65/5

p=13

Equal roots

=>D=0

p(x^2+x)+k=0

px^2+px+k=0

D=b^2-4ac

=(p)^2-4xpxk=0

=(13)^2-4x13xk=0

=169-62-k=0

=107-k=0

=-k=-107

= k=107

Answer 2

The value of k is 13 / 4.

• The first quadratic equation is given as 2x² + px + 15 = 0 - (i)

Given that,

Root of the equation = - 5

• Since - 5 is a root of equation (i), one of the values of x is - 5.

Now, putting x = - 5 in the equation, we get,

2 × (- 5)² + p × (- 5) + 15 = 0

Or, 2 × 25 - 5p + 15 = 0

Or, 50 - 5p + 15 = 0

Or, 65 = 5p

Or, p = 65 / 5

Or, p = 13

∴  The value of p in the given quadratic equation is 13.

• The second equation is given as p (x² + x) + k = 0

Or, px² + px + k = 0

Substituting p with 13 in this equation, we get,

13x² + 13x + k = 0 - (ii)

• It is given that the roots of the equation are equal.

Now, the roots of a quadratic equation are equal when its discriminant is equal to zero.

• Discriminant = b² - 4ac

For roots to be equal,

b² - 4ac = 0

• In equation (ii), b = 13, a = 13, c = k

∴   (13)² - 4 × 13 × k = 0

Or, 169 - 52k = 0

Or, 169 = 52k

Or, k = 169 / 52

Or, k = 13 / 4

∴   The value of k is 13 / 4.