Question

State whether the following quadratic equations have two distinct real roots. Justify your answer,x²-3x+4=0​

Answer 1

Answer:

a = 1, b = –3 and c = 4

Now, D = b2 – 4ac = (–3)2 –4(1) (4) = 9 – 16 = – 7< 0

Hence, the equation x2 –3x + 4 = 0 has no real roots.

(ii) Given equation is, 2x2 + x – 1 = 0

On comparing with standard equation we have,

a = 2, b = 1 and c = –1

Now, D = b2 – 4ac = (1)2 – 4(2) (–1) = 1 + 8 = 9 > 0

Hence, the equation 2x2 + x – 1 = 0 has two distinct real roots.

Answer 2

Answer:

x2-4x+1x+4=0

x(x-4)1(x+4)=0

(x-4) (x+1)=0

x-4=0,x+1=0

x=4,x=-1