Find the discrinmant of 3x^2 - 7x + 2 = 0
and what does discrimnant mean

Question

Find the discrinmant of 3x^2 - 7x + 2 = 0
and what does discrimnant mean

anonymous · Answer

Please help

parthkohli · Answer

Discriminant in $ax^2 + bx + c = 0$ is $b^2 - 4ac$

parthkohli · Answer

Here the discriminant would be $(-7)^2 - 4(3)(2)$

anonymous · Answer

25?

anonymous · Answer

what does this word mean?

parthkohli · Answer

Yeah. Discriminant determines the number of solutions in a quadratic equation :)

parthkohli · Answer

If the discriminant is a perfect square, then we have two integer solutions.

anonymous · Answer

what does it mean when its 25

unklerhaukus · Answer

For a quadratic equation of the form
$$ax^2+bx+c=0$$
The discriminant is some times written like this$$\Delta=b^2-4ac$$

aravindg · Answer

well the discriminant is a no  that gives us the idea how the roots of the quadratic equation will be

unklerhaukus · Answer

the quadratic formula
used to finds solutions of x in a quadratic equation
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} =\frac{-b\pm\sqrt\Delta}{2a}$$

aravindg · Answer

if the discriminant is irrational the roots are irrational conjugates ,
if the discriminant is 0 there is only 1 root , 
if discriminant >0 there are 2 real and distinct roots , 
if discriminant <0  roots are imaginary 

hope that clears ur doubt

unklerhaukus · Answer

the discriminant is used to determine the number of solutions for x 
ie the number of times the quadratic curve cuts the x-axis


$\Delta >0 $    if the discriminant is a positive number there are 2 solutions,
ie the parabola cuts the x-axis twice

$\Delta =0 $  if the discriminant is zero there is one solution
ie the parabola touches the x-axis at one point

$\Delta <0 $   if the discriminant is a negative number there are no real solutions 
ie the parabola does not cut the x-axis

unklerhaukus · Answer

if the discriminant is a positive number
 that is also a square number
 the solutions/roots of the equation are rational numbers 
the points where the parabola cuts the x-axis are rational point on the x-axis

unklerhaukus · Answer

for example 
$$4x^2 - 3x -1 = 0$$
$$\Delta=b^2-4ac=(-3)^2-4\times(4)\times(-1)$$$$\qquad\qquad\qquad=9+16$$$$\qquad\qquad\qquad=25$$

$\Delta>0$ so there are two solutions
$25$ is also a square number so the roots are rational 


the quadratic formula 
$$x=\frac{-(-3)\pm\sqrt {25}}{2\times-3}=\frac{3\pm5}{-6}$$
$$x_{1,2}=-\frac {4}{3},\frac 13$$

which are two rational roots