Question

45. a)Discuss the nature of the solutions of x +2x+5 b) x2 +x-12.
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Answer 1

a

• x+2x+5
• 3x+5

b

• x² +x-12.
• x² +4x-3x-12
• x(x+4)-3(x+4)
• (x+4)(x-3)

Answer 2

Answer:

"We know that while finding the root of a quadratic equation ax

2

+bx+c=0 by quadratic formula x=

2a

−b±

b

2

−4ac

,

if b

2

−4ac>0, then the roots are real and distinct

if b

2

−4ac=0, then the roots are real and equal and

if b

2

−4ac<0, then the roots are imaginary.

Here, the given quadratic equation x

2

−2x+3=0 is in the form ax

2

+bx+c=0 where a=1,b=−2 and c=3, therefore,

b

2

−4ac=(−2)

2

−(4×1×3)=4−12=−8<0

Since b

2

−4ac<0

Hence the roots are imaginary or no real roots. "