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General form of Quadratic Equation ---> ax2+bx+c

alpha+ Beta =-b/a;   alpha x beta = c/a

Given a=p; b=-2; c=3p

           alpha+beta=alpha x beta

      so, 2/p=3

           p=2/3

2(1)²-3(1)-4 =2×1-3×1-4 =2-3-4 =-1-4 =-5

Truck travels 14 km in 25 mins. Distance covered in 5 hours i.e. 5*60 mins = 300 mins is 300*14/25 = 168 km

Given, PQR is a triangle and <Q =90 degree 

And PQ = 12 cm 

       PR = 13 cm

We know that the area of right angle triangle = 1/2 ( product of legs)

But one leg QR is not given here

 So by Pythagores theorem 

                       (PQ)^2 + (QR)^2 = (PR)^2

                     = (12)^  + (QR)^2 = (13)^2

                     = 144 + (QR)^2    =169

              So, (QR)^2= 169-144

                or, (QR)^2=25

               so, QR = 5 cm

Now Area of right anged triangle PQR= 1/2 X 5 X 12

                                                             =30 sq.cm Answer

Given , The machine fills 675 bottles in 5 hours .

       so, the machin will fill 1 bottles in 5/675 bottels 

      so, the machine will fill 1890 bottels in 5/675 X 1890

                                                               = 14 hours

Therefore the machine will take 5 hours to fill 1890 bottles.

Part of tank filled by first tap in one hour = 1/10

Part of tank filled by second tap in one hour = 1/15

Part of tank filled by first and second tap in one hour = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6.

So the tank will be filled in 6 hours when both taps are turned on simultaneously.

An equation of the form  ax^2 + bx + c = 0 where a, b and c are all real and a is not equal to 0, is a quadratic equation.

(i) (5x-3)(x+5) = x(2x+1)

5x^2 - 15 + 22x = 2x^2 +x

3x^2  + 21 x - 15 = 0

As per the definition this is a quadratic equation.

(ii)  x^2 + 7x + 5 = (x+7)^2

x^2 + 7x + 5 = x^2 + 14x + 49

7x + 44 = 0

This is not a quadratic equation , since there is no x^2 term.

(c) as signs of irrational parts may cancel out ...same goes for non  irrational part...

HCF of a number is number itself hence 306