Use the drop-down menus to choose steps in order to correctly solve 3+4d−14=15−5d−4d for d.
Answers
Answer:
★QuestioN★:−
Discuss the nature of the roots of the following equations.
\bf{4x^2-12x+9=0}4x
2
−12x+9=0
\pink\bf{\bigstar{AnsweR}\bigstar:-}★AnsweR★:−
✧To find the nature of roots, we have to use the formula for discriminant.
\bf{Discriminant = b^2 - 4ac}Discriminant=b
2
−4ac
✧Here,
:\longrightarrow\green\bf{a=4~,b=-12~, c=9}:⟶a=4 ,b=−12 ,c=9
✧On applying formula,
:\implies\red\bf{b^2-4ac=(-12)^2-4\times4\times9}:⟹b
2
−4ac=(−12)
2
−4×4×9
:\implies\red\bf{144-4\times4\times9}:⟹144−4×4×9
:\implies\red\bf{144-144}:⟹144−144
{\boxed{\underline{\bf{\sf{\red{\bigstar0\bigstar}}}}}
✧Here,
✧D = 0
✧That's why the equation have two equal real roots!!
\huge{\boxed{\underline{\bf{\sf{\red{\bigstar{Extra~Info:-}\bigstar}}}}}
⟿ Nature of roots are based on the discriminant.
⟿ According to that, three types are there. They are,
Two distant real roots.
Two equal real roots.
No real roots.
⟿ Nature of roots of quadratic equations by using quadratic formula,
Two distant real roots if, b² - 4ac > 0.
Two equal real roots if, b² - 4ac = 0
No real roots if, b² - 4ac < 0.