Question

please help me to do this question ​

Answer 1

Answer:

Answer: (b) 5/4

Step-by-step explanation:

Check the images for explanation

Answer 2

Question : -

If one zero of the quadratic polynomial, (k-1)x²+Kx+1 is -4 then the value of k is

• (a) (-5)/(4)
• (b) (5)/(4)
• (c) (-4)/(3)
• (d) (4)/(3)

ANSWER

Given : -

One zero of the quadratic polynomial, (k-1)x²+kx+1 is -4

Required to find : -

• value of k ?

Formula used : -

Quadratic formula !

Let consider a polynomial p(x) = ax²+bx+c for which the zeroes are x,y then

• x = (-b+√[b²-4ac])/(2a)
• y = (-b-√[b²-4ac])/(2a)

Solution : -

One zero of the quadratic polynomial, (k-1)x²+kx+1 is -4

So,

(k-1)x²+kx+1 = 0

The standard form of a polynomial is ax²+bx+c = 0

Comparing both the polynomials !

(k-1)x²+kx+1 = 0 ax²+bx+c = 0

Here,

a = (k-1)

b = k

c = 1

Since, one of the zero of the polynomial is -4

so,

• x = -4

Using the formula;

x = (-b+√[b²-4ac])/(2a)

-4 = (-[k]+√[(k)²-4(k-1)(1)])/(2[k-1])

-4 = (-k+√[k²-4k+4])/(2k-2)

By cross multiplication

-4(2k-2) = (-k+√[k²-4k+4])

-8k+8 = -k+√[k²-4k+4]

-8k+8+k = √(k²-4k+4)

8-7k = √([k]²-2[k][2]+[2]²)

8-7k = √([k-2]²)

8-7k = k-2

-7k-k = -2-8

-8k = -10

-(8k) = -(10)

8k = 10

k = (10)/(8)

k = (5)/(4)

Therefore,

• value of k = (5)/(4)