Question

Number of zeroes of the polynomial √3x3 - √3 ( )​

Answer 1

Answer:

Let

′

sunderstandthequestionfirst

➨ This question says that we have to find the equation of line which passes through the point of intersection of the lines x+2y-3 = 0 and 3x+4y-5 = 0 and it is perpendicular to the line x-3y+5 = 0.

{\large{\bold{\sf{\underline{Given \; that}}}}}

Giventhat

➨ Line passes the point of intersection of the lines x+2y-3 = 0 and 3x+4y-5 = 0

➨ It's perpendicular to the line x-3y+5 = 0.

{\large{\bold{\sf{\underline{To \; find}}}}}

Tofind

➨ Equation ( given question )

{\large{\bold{\sf{\underline{Solution}}}}}

Solution

➨ Equation = y + 3x + 1 = 0

{\large{\bold{\sf{\underline{Assumptions}}}}}

Assumptions

➨ Point p(r,m) is point of intersection

➨ a is the slope which passes through the point of intersection of the lines x+2y-3 = 0 and 3x+4y-5 = 0 and it is perpendicular to the line x-3y+5 = 0.

{\large{\bold{\sf{\underline{Full \; Solution}}}}}

FullSolution

~ Firstly let us find the point of intersection of lines x+2y-3 = 0 and 3x+4y-5 = 0

➨ Point p(r,m) is point of intersection

➨ x + 2y - 3 = 0

➨ r + 2m - 3 = 0

➨ r = 3 - 2m Equation 1

➨ 3x + 4y - 5 = 0

➨ 3r + 4m - 5 = 0

➨ r = (5-4m) / 3 Equation 2

~ Now from equation 1 and 2

➨ 3 - 2m = (5-4m) / 3

➨ (3 - 2m)3 = (5-4m)

➨ 3(3 - 2m) = (5-4m)

➨ 9 - 6m = (5-4m)

➨ 9- 5 = 6m - 4m

➨ 4 = 2m

➨ 4/2 = m

➨ 2 = m

Henceforth, the value of m is 2

~ Now let's find the value of r

➨ r = (3 - 2)m

➨ r = (3 - 2)2

➨ r = (3 - 2) × 2

➨ r = 3 - 4

➨ r = -1

Henceforth, the value of r is -1

{\green{\frak{Henceforth, \: (-1,2) \: is \: intersecting \: point}}}Henceforth,(−1,2)isintersectingpoint

~ Now let's see the slope

➨ x - 3y + 5 = 0

➨ -3y = -x - 5

➨ y = (x+5)/3

➨ y = (x/3) + (5/3)

➨ Henceforth, we get y = (x/3) + (5/3) at the place of x-3y+5=0. And it's a form of y = mx + c

➨ Therefore, slope of line is 1/3 now

~ Let's find the value of Assumption a

➨ a × 1/3 = -1

➨ a = -1 × 3

➨ a = -3

~ Now let's find the final result ( Equation )

➨ y - 2 = (x+1)(-3)

➨ y - 2 = -3x - 3

➨ y + 3x = -3 + 2

➨ y + 3x = -1

➨ y + 3x + 1 = 0

{\green{\frak{Henceforth, \: y + 3x + 1 = 0 \; is \; equation \; or \; final \; result}}}Henceforth,y+3x+1=0isequationorfinalresult