Question

Instruction:- Attempt all the questions as per given instructions.
प्रश्न 1 शेषफल प्रमेय से PA)-4x3x121-) को (-) से भाग देने पर शेषफल
ज्ञात कीजिए।
अंक-03
Q.1
Find the remainder by Remainder theorem il p(x) = 4x+3x2+2x-9 is
divisible by (x-2)
प्रश्न 2 के किस मान के लिए रागीकरण निकाय Ny= और 31+y= [ का द्वितीय
हल होगा।
अंक-03
0.2
For what value of the given system of equation KX+2y =s and
3x+y=1 have unique solution,
प्रश्न 3 वर्ग समीकरण 3x2 +74 | I = () के गूलो का योगफल और गुणनफल ज्ञात
कीजिए।
अक-03
Q.3
Find the sum and product of roots of the quadratic equation
3x247x+1=0
प्रश्न 4 वर्गसमीकरण 2x245x15= () का विभेदक ज्ञात कीजिए।
अंक-03
Q.4 Find the Discriminate of the quadratic equation 2x +5x+5= ()
प्रश्न 5 वर्ग समीकरण 6x2 | X-2= () को सूत्र विधि से हल कीजिए।
अंक-04
(1.5
Solve the quadratic equation 6x2 +X-2 = ( by formula method.
प्रश्न 6 समीकरण को हल कीजिए (विलोपन विधि से)
4x-Sy= 20 और 3-5y= 15
अक-04​

Answer 1

Answer:

5 Answer = 6×2+x-2 = 0

12+x-2 = 0

x+12-2 = 0

x+10=0

x = - 10

Answer 2

Solution 1) :-

we know that, according to remainder theorem , when p(x) is divided by (x - a) , remainder will be p(a) .

So,

→ p(x) = 4x³ + 3x² + 2x - 9

→ p(2) = 4(2)³ + 3(2)² + 2*2 - 9

→ p(2) = 32 + 12 + 4 - 9

→ p(2) = 39

therefore, when p(x) is divided by (x - 2) remainder will be 39 .

Solution 2) :-

given equations ,

→ kx + 2y - 5 = 0

→ 3x + y - 1 = 0

comparing them with a1x + b1y+ c1 = 0 and a2x + b2y + c2 = 0 we get ,

• a1 = k
• b1 = 2
• c1 = (-5)
• a2 = 3
• b2 = 1
• c2 = (-1)

So,

→ For unique solution = a1/a2 ≠ b1/b2 .

putting values,

→ k/3 ≠ 2/1

→ k ≠ 6 .

therefore, at k ≠ 6 , the given system of equations will have a unique solution .

Solution 3) :-

we know that, for a quadratic equation ax² + bx + c = 0,

• sum of roots = (-b/a)
• product of roots = c/a .

so, comparing given equation 3x² + 47x + 1 = 0 with ax² + bx + c = 0, we get,

• a = 3
• b = 47
• c = 1

then,

→ sum of roots = (-b/a) = (-47/3)

→ product of roots = c/a = (1/3)

Solution 4) :-

→ Discriminate (D) = b² - 4ac

→ D = (5)² - 4 * 2 * 5

→ D = 25 - 40

→ D = (-15)

Learn more :-

solution of x minus Y is equal to 1 and 2 X + Y is equal to 8 by cross multiplication method

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