Question

If p and q are the zeroes of the polynomial 2x^(2) - 5x - k such that p-q=(9)/(2) find the value of k

Answer 1

Answer:

Heya !!!

P(X) = X²-5X+K

Here,

A = 1 , B = -5 and C = K

Given that,

P and Q are the two zeroes of the given polynomial.

Therefore,

Product of zeroes = C/A

P × Q = -K/1 --------(1)

Sum of zeroes = -B/A

P + Q = -(-5)/1

P + Q = 5 --------(2)

And,

P-Q = 1 ---------(3)

From equation (2) we get,

P + Q = 5

P = 5-Q --------(4)

Putting the value of P in equation (3)

P - Q = 1

5-Q - Q = 1.

-2Q = 1-5

-2Q = -4

Q = -4/-2

Q = 2

Putting the value of Q in equation (4) we get,

P = 5-Q

P = 5-2 = 3

P = 3 and Q = 2

Now ,

Putting the value of P and Q in equation (1)

P × Q = - K

3 × 2 = - K

K = 6

Hence,

The value of K is 6.

HOPE IT WILL HELP YOU...... :-)

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Step-by-step explanation:

Answer 2

Answer:

$k = 7$

Step-by-step explanation:

Taking p as m and q as n:

Let m and n be the roots of the equation

According to the properties,

$m + n = \frac{ - b}{a} = \frac{5}{2}$

$mn = \frac{c}{a} = \frac{ - k}{2}$

Now squaring the first property and finding the value of m²+n²:

${m}^{2} + {n}^{2} = \frac{25}{4} + k$

Then squaring m-n = 9/2 and substituting and simplifying we get:

$k = 7$