Question

Which two values of x are roots of the polynomial below 4x^2-6x+1

Answer 1

Step-by-step explanation:

• Just apply the quadratic formula $x=\frac{-b \left \ {{+} \atop {-}} \right. \sqrt{b^{2}-4ac} }{2a}$

• Your equation is $4x^2-6x+1$
• Every quadratic equation follows the general form $ax^2+bx+c$

• In this case $a=4,b=-6,c=1$
• Substitute into the quadratic formula:
• $x=\frac{-(-6) \left \ {{+} \atop {-}} \right. \sqrt{(-6)^{2}-4(4)(1)} }{2(4)}\\x=\frac{6 \left \ {{+} \atop {-}} \right. \sqrt{36-16} }{8}\\x=\frac{6 \left \ {{+} \atop {-}} \right. \sqrt{20} }{8}$ Now take note that the square root of any number gives a (+) and (-) result, so two different answers
• $x=\frac{6 + \sqrt{20} }{8} ,and\\x=\frac{6 - \sqrt{20} }{8}$ are the answers