we know that In a quadratic equation ax²+bx+c=0 the term (b² - 4ac) is called the "discriminant" because it can "discriminate" between the possible types of answer: so (b² - 4ac) > 0 we get two real solutions (b² - 4ac) =0 we get just ONE real solution (b² - 4ac) < 0 we get complex solutions or no real solutions
part 1) 5x²+2=4x 5x²-4x+2=0 a=5 b=-4 c=2 (b² - 4ac)=(-4)²-4*(5)*(2)------> 16-40-----> -24 so (b² - 4ac) < 0-------> No Real Solutions
the answer Part 1) is No Real Solutions
part 2) 3(x+5)²=-2 3(x²+10x+25)=-2 3x²+30x+75=-2 3x²+30x+77=0 a=3 b=30 c=77 (b² - 4ac)=(30)²-4*(3)*(77)------> 900-924 -----> -24 so (b² - 4ac) < 0-------> No Real Solutions
the answer Part 2) is No Real Solutions
part 3) 4x²-16x=0 a=4 b=-16 c=0 (b² - 4ac)=(-16)²-4*(4)*(0)------> 256 so (b² - 4ac) > 0-------> Two Real Solutions
the answer Part 3) is Two Real Solutions
part 4) 3x²+24x=-48 3x²+24x+48=0 a=3 b=24 c=48 (b² - 4ac)=(24)²-4*(3)*(48)------> 0 so (b² - 4ac) =0 -------> One Real Solution
