Math, asked by ruplalbaburam, 10 months ago

MATHEMATICS
WORKSHEET -2
QUADRATIC EQUATIONS
CLASS:10
1. The roots of the equation x' + 7x + 10 =0 are
(a) 2 and 5 (b)-2 and 5 (c)-2 and -5 (d) 2 and -5
2. If the equation x + 4x + k = 0 has real and distinct roots then
(a) k <4 (b) k > 4 (c) k= 4 (d) k= - 4

Answers

Answered by sridharhs2008
11

Answer:

dude I think the first question is wrong because u can determine the roots based on power or degree of equation

Step-by-step explanation:

hey here u go for rest of it

Attachments:
Answered by Anonymous
105

{\underline{\sf{Question}}}

1. The roots of the equation x²+ 7x + 10 =0 are

(a) 2 and 5 (b)-2 and 5 (c)-2 and -5 (d) 2 and -5

2. If the equation x² + 4x + k = 0 has real and distinct roots then

(a) k <4 (b) k > 4 (c) k= 4 (d) k= - 4

{\underline{\sf{Theory }}}

For a Quadratic equation of the form

ax²+bx+c= 0 , the expression b²-4ac is called the discriminant.

Nature of roots

The roots of a quadratic equation can be of three types.

  1. If D>0, the equation has two distinct real roots.
  2. If D=0, the equation has two equal real roots.
  3. If D<0, the equation has no real roots.

{\underline{\sf{Solution}}}

Part -I

Let the given quadratic equation be f(x) ⇒ f(x)= x²+ 7x + 10

We have to find roots of given equation

 \sf \: f(x) = 0

 \implies \sf  {x}^{2}  + 7x + 10 = 0

 \sf \implies  {x}^{2}  + 5x + 2x + 10 = 0

 \sf \implies x(x + 5) + 2(x + 5) = 0

 \sf \implies(x + 5)(x + 2) = 0

 \sf \implies \: x + 5 = 0 \: or \: x + 2 = 0

 \sf \implies \: x =  - 5 \: or - 2

Part -II

Given : The equation x² + 4x + k = 0 has real and distinct roots.

 \sf \implies \: D &gt; 0

 \sf \implies \: b {}^{2}  - 4ac &gt; 0

 \sf \implies \:  {4}^{2}  - 4k &gt; 0

 \sf \implies16 &gt; 4k

 \sf \implies \: k &lt; 4

Similar questions